Being a power helps so that he can use it while it Turret Mode. Also, he isn't giving up his power phase, he is giving up 1 power use. With Turret Mode or APS, he can still use another power. While this is a specific case, Bunker can single-handily take out Blade's full hp MPD and Backlash Field by himself in a single turn.
This power might also be better to use anyway. If destroying a specific Ongoing will drastically increase you survivability and thereby increase your overall damage, it will probably be better than using another power anyways.
Not entierly. If he plays Gatling Gun, Omni-Cannon, or Auxiliary Power Source, he didn't lose anything by the loss of a power.
Actually, since he is immune to environment damage, playing Adhesive Foam Granade isn't such a bad idea. Also, External Combustion essentially gives you the damage that you loss (obviously, if you have to see if taking 2 damage is worth it).
I am not trying to say that the power is great, everyone has their own opinion (and I am not saying mine). However, there are a couple things to keep in mind.
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Not every hero uses their base power every turn of every game. There are many heroes that can very quickly put down a power that is better than their base. You shouldn't be thinking that Bunker should be using it every turn, but having that extra utility when you need it can be very helpful.
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The question is whether the loss of Initialize worth the Ongoing destruction. This is up to each individual player, and how often they use Initialize. If they depend on it, then this can be a big hit. If the don't, becuase they are using damage dealing powers, then just having the option of more utility can be a big help.
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Giving a damage dealer a way to get rid of Ongoings at will would be very OP. Therefore, he needs a Mode card in his hand. Sometime it works, sometimes it doesn't. There is no difference between this or any other hero not drawing their Ongoing destruction, except there are a lot more Mode cards in Bunker's deck, than Ongoing destruction in any other heroes deck.
However, the key idea behind promor character is not to increase their power, but to change they way they play. Whether you like B:EoW or not, I tihnk it does this quite well.