What rational person looks at the mess that's entirely their own fault, ignores any offers of kindness, and decides to kill people for fun?

Rationality? That's rich coming from someone who denies the very arguments given to us by the game (and in an admittedly poor way as well) to attempt to frame (not encourage, not condone) Adachi's behavior:

• Let's start with the easiest one - ignoring any offers of kindness: Adachi can't understand kindness (and empathy, in general) from people because he himself was denied that during his formative years. In his own words and using the P4G anime flashback sequence: Adachi's parents never gave a shit about their kid so long as he had good grades. If you're familiar with most Asian families, this is how they treat their kids. Furthermore, by the end of P4/P4G (on the Golden Ending) as well as in Adachi's ending in P4AU, he acknowledges that the time he spent with the Dojimas was "fun" and he appreciated them
• "A mess that's entirely their fault and killing people for fun": Adachi is a broken man because his entire life didn't go as planned: He studied his butt off at an elite high school (in one of his SL dialogues), got to a (supposedly) prestigious university, joined the force as an elite member and, for some badly explained "incident", got shafted to a remote area where there's nothing interesting to do aside from going to Pub Shiroku and get wasted. He followed what many parents around the world peddled to their kids to the letter and didn't get a decent ROI from it. Of course he'll be resentful - and compounded with the earlier point about kindness, he'll become murderous.

The closest real-life example of an "Adachi" archetype is Jennifer Pan. Here's a documentary about what she did and the circumstances that led her to do it: Jennifer's Solution.