Death Wish (1974) - Is Paul Kersey *really* just snapping?

Okay, so I just watched 'Death Wish' (1974) and wow... heavy stuff. Like, seriously, brutal. I went in totally blind, knew nothing about it other than vaguely the premise. It's about this architect, Paul Kersey, whose wife is murdered and daughter assaulted, and he basically turns into a vigilante, cleaning up the streets of New York. But here's what I'm thinking... is it JUST revenge? I'm not convinced. The scene where he's getting mugged the FIRST time after he gets the gun seems... staged, almost? Like, he *lets* it happen. Then he gets mad when he gets mugged again soon after. Then he starts actively seeking out crime. My theory is that the trauma of what happened to his family unlocked something in him. Maybe he's always had a violent side, suppressed by his comfortable life. The pacifist architect was just a facade. It's like the 'crime' gives him an excuse to unleash that... something. He's not just avenging his wife, he's enjoying it? Maybe too strong a word, but like, he's finding some kind of twisted satisfaction? I mean, think about it. He goes from being a normal dude to this cold-blooded killer pretty fast. Sure, trauma plays a part, but the way he so quickly embraces it... it feels deeper than just grief and anger. Plus, the transformation is so drastic. Doesn't it seem a little unrealistic? Maybe it's just bad writing, but I think it could be deeper. Anyway, just my thoughts. I'm curious what you guys think. Am I overthinking this, or is there something more going on with Kersey's transformation? I'm new to older movies so, not sure how deep to go on these lol.