You have that the wrong way round, tools go back to your hand, styles don't. But I have no idea why.
Would it be unbalancing? Probably not and if it makes your friend happier playing with him do it, just be sure to tell people of any house rules before you start playing (and don't submit any of the games to the stats project, house rules are not encouraged there).
One of the reasons I can think of is that Styles of Meditation which allow you to search for the style you desire in both the deck and trash. Where Tools can't be searched for at all. However you can retrieve all equipment cards with Salvage Yard, at the same time though since tools don't usually get destroyed it isn't too common to retrieve a lot of your equipment cards from the trash
Your friends will love you for it and love you even more if you can keep the grease gun going since it's an equipment. But yeah I believe it's meditation's existence that is the defining factor and to diversify mechanics so tools and style dont play the same but complement each other. Fixer has his shining moments either way last game I played with him a player whined I was stealing all the sunshine with fixer I was laughing thinking on how people perceive fixer on this forum.
He is pretty old. His memory fails him at times. Probably was killed by Alzheimer's and not at the hands of Iron Legacy as per popular belief. He has to meditate every day to slow his memory's decay.
Part of true zen mastery is learning to let things go. Whatever happens shall happen, and clinging to the past will not accomplish everything. All that matters right now is the opponent in front of you. Seek the purity of perfection, not the perfection of purity. Then you will be cleansed...