I use the same and it irons out the bad without altering bunker too much.
I was very much like you for a long time, I don't like the mechanic of discarding cards (one reason I am not a big fan of NightMist or Parse). Recently, Gatling Gun has become one of my favorite cards, and I wish there were more than 2 in the deck. It offers a somewhat nice replacement as a power for Flak Cannon (a little less for Grenade Launcher). You sacrifice 1 damage for seeing more of your deck.
Given, there are some downsides, you don't do the damage until next turn, and you pay the cost before getting the benefit. However, having both Gatling Gun and Flak Cannon out that's 5 damage every turn (7 or 9 with plus to damage), without your play phase. Honestly, I feel that's quite a bit, especially since you can still play more cards to setup for something else.
The sad thing is that I actually enjoy playing Nightmist and Parse, even with their discard mechanics. The Gatling Gun feels different somehow. I guess it's because it's a passive effect I have to keep paying for rather than an active effect like a power or card play. It feels like paying taxes just to get a smallish hit.
And yes, I know that this is a completely irrational opinion. I guess I'll have to play him more to get past my dislike of the thing.
I look at Gatling Gun as an extra use of Ra's base power, at the cost of discarding one of Bunker's copious useless cards. ;)
I agree with this … to an extent.
Bunker is perhaps the ultimate example of the value in playing your hand versus playing your deck, while at the SAME_TIME requiring one to know about the various possibilities of his deck in order to understand what his hand can actually achieve. Bunker is a Tactician and forces me to make a lot of tactical decisions. The very best I can do with my hand at the moment may not be the best way to set up Bunker to be valuable in the future.
All this is true for most if not all of the heroes, but I think Bunker is a prime example. If you've got a Gatling Gun, Flak Cannon, and Turret Mode in hand, do you play the Flak Cannon now in order to do immediate damage with an eye towards possibly getting into Turret Mode, or do you play the Gatling Gun knowing that it won't do anything immediately, but if you draw into Recharge Mode, Omni Cannon, Heavy Plating, and/or Adhesive Foam grenade then you're setting yourself up to be able to do regular damage while still doing something else (tanking, building to a big attack, environment control)? How long do you think the game will last? How important are the various things you can do? What are the other heroes going to do? Like I said, these are questions most if not all of the heroes might ask themself, but Bunker is ALL ABOUT asking these questions.
Earlier today I had a Grenade Launcher, an Omni-Cannon, and Gatling Gun on the table, and a Maintenance Unit and Turret Mode in my hand. Normally I would feed the Cannon and throw a Grenade, but this time I played the MU and followed it the next turn with Turret Mode. I fed the card I got after the MU turn to the Gatling Gun. There was something cool about knowing that for the next little while, I could count on healing for 2HP and blasting things for 3, 3, and 2 damage each round, and I had SS Tachyon throwing things out from under my deck.
After a couple of rounds, I killed Turret Mode and just played it out. It didn't feel like a loss of options, but a guarantee of a specific pattern that would be available to me until I either lost the equipment or decided to get out of that mode.
I think one day I'll play Bunker with the specific goal of playing all three modes as much as possible, and see how it goes. Maybe he'll click to me then.
But I think Andy nailed it above. Bunker seems to be about going to war with the army you have, not the army you want.
And credit to Silverleaf, I think, who, if I recall correctly, was the first to articulate that strategy.
The strategy of balancing strategy against tactics? 
When I was creating my hero ranking system I wanted to value different types of damage dealing, and I divided it by amount of setup.
Starting damage: you start your turn with 0-1 card in play.
Mid-range damage: start your turn with 2-3 cards in play.
High End damage: How crazy can you get with lots of cards in play.
Bunker is interesting because he is solid at any level, but he can excel at mid range setups if you are willing to forego building up any farther.
The number of valid 3-4 card builds are really awesome with Bunker, and weighing between good Turret builds or sticking to no mode is an interesting process.
His drawback is he can really punish a player that cimmits too early or too late.
That was the impetus behind our house rule, making him more forgiving by allowing you to switch modes and keep your modes in hand.
I don't use that house rule anymore, simply because it taught me how to play him well enough to no longer need it.
If you plan to leave Recharge Mode up for any significant amount of time (and you should, most of the time that you play it at all), you'll get *3* card draws per turn, on every turn after the first. 1 extra from Recharge itself, and 1 extra for forgoing (by necessity!) your play and power.
Upgrade Mode got itself upgraded a bit in my opinion when I realized what you can do by (after a few rounds of double-play), playing Turret Mode as the second card. Extra play *and* two powers on that turn!
Granted, most games I still won't play either of them, but they're not as bad as you think. A lesson that is true about *most* cards one never plays...
I don't remember if I was the first to present it here, but I'm sure it wasn't my idea originally. I have been somewhat vocal in my support of said strategy though! 
FWIW I used to dislike Bunker. I didn't think he was bad, just boring as he didn't fit my preferred play style. Since the app I've warmed to him a fair but - he'll never be a favourite but I don't mind playing him now, especially as I have 2-4 other heroes to keep me entertained in every Bunker game in the app.
He's like visionary to me now. Not my favorite, and I'll never feel like I'm getting the most out of him, but I can play him effectively and he does the job. His 2 main guns are effective, and they do their jobs, but I always feel like I'm missing something
I love the Bunks, but part of that is due to him being my first hero. I tend to go for the cards with a more immediate effect since that fits with my play style more, and so I'm not a fan of Upgrade Mode since you have to wait a whole round to actually benefit from it. I do actually like Gatling Gun. If I don't have Flak or Grenade, I can do consistant damage while using Initialize to increase my options and feed the Gatling Gun. I like both of Bunker's promos. They're both situational, but they're very useful for those situations. G.I. Bunker is my favorite for both his power and backstory.
This is OT (of the OT tangent we're already on…), but where can you find backstory on the promos?
At least for the promos released on the SotM app it's on the multiverse page for SotM. http://sentinelsofthemultiverse.com/multiverse/heroes/bunker
Also, the wiki SotM.wikidot.com also will list out what is known.
Note that not all Promo bios are avaliable. They seem to be comming out (and old ones being revised) as they are released on the App.
You can also find them within the game itself, by going into the Multiverse option, clicking on a hero with a variant you have unlocked and on the top right there will be a variant button you can click.
Having played Kaargra I think that Fickel Fans is a good idea with an average implementation. The idea is to give a catch up to the losing side since the winning side probably has snagged some Titles and is not only winning but getting stronger. And the H in the card makes sense, since more Heroes means more chances of getting additional points and Kaargra and other Villains are doing more damage (so more points).
But, in general, catch up mechanics that when triggered change who is in the lead or decide who is the winner are bad. Catch up mechanics should keep you in the game and avoid lame duck situations, not be exploited or help you win the game by losing (if the game is not about that).
IMO what Fickle Fans should do is either bridge the gap of points between the sides or make it harder for the winning side to gain points. But the losing side should still be either losing or tieing after the card is played. There are a lot of ways to go about this. Like "Move X favour tokens from the pool with the most tokens to the pool with the least tokens, where X = the difference between the winner minus the loser divided by 2, rounded down". While not as simple as just moving H tokens, it's not that bloated or complicated and mitigates game deciding situations (the losing side still needs to do stuff on their own to win).
A different approach, ignoring points and considering Titles: "Remove X favour tokens from each side where X = the number of titles that side has gained". Or maybe even just removing tokens from the pool with the most of them.
Rewarding the players for planning when that card to comes into play, IMO, hurts the experience more than what the mechanic achieves. The focus as a Hero should be kicking butt in the Arena, not thinking about the show's rating or when they are going to commercials.
unless you are using deck manipulation you don't plan on Fickle Fans, esp. when you are close enough that it can end the game.
If you are using deck manipulation then okay, you are outplaying the Arena Master at her own game. Otherwise you are banking on a card coming at the right time, which is a risky move.
It is a much better approach to get out in front and just push through. Intentionally staying close but behind can work, but it can cost you the match if the card doesn't come in time.
Waiting for fans while intentionally under earning points is like not playing cards because at any time La Capitan could destroy a few of them. Getting out in front is almost always the better option.
Your argument hinges on the assumption that Fickle Fans fills a "Catch Up Mechanic" type role.
What if I told you that Fickle Fans isn't a "Catch Up Mechanic" and never was intended to be so?
I'll let you stew on that for a bit.