I agree to an extent. I see it less as Billy consciously choosing DH's goals, but more as the result of his personality failings. It's classical tragedy — a man undone by his own fatal flaws. In Billy's case, he's an introvert who really doesn't seem to understand people or the world. It's not so much the introversion itself that undoes him (believe it or not there are perfectly well-adjusted introverts!), but his general inability to deal with other people. He's terribly naive about evil — he seems to see it as his path to becoming significant and addressing past wrongs — but seems to have little real idea of what being evil actually means. He's perfectly right about homelessness being a symptom of a greater disease (I'm from a city with a homelessness problem mostly due to poor government decisions that left many people with mental and substance abuse problems nowhere to go but the streets, so that bit really rang true for me), but his solution for it is completely unrealistic. He wants to fight the wrongs that plague humanity but he doesn't know how. He's obsessed with Penny, but the fact she may have her own problems comes as a complete revelation to him. He never realises he doesn't have to impress her to win her over — just be himself. He's completely blind to the fact she may be falling for him a little. He lacks the emotional maturity to handle love and jealousy.

One of the things he wants to do with his freeze ray is to 'stop the pain.' He's someone who obviously has had a lot of pain in his past; he sees himself as a 'dork, a geek, a failure,' and he keeps looking for ways to soften the blow of bruising himself on the world. Unfortunately, his end solution is to completely lose himself. DH doesn't hurt, only Billy does, and he's only Billy at home. 

There are a lot of ironies in his story. One of them is that it appears he and Penny are perfectly compatible, and if he'd been able to read her better or had spoken to her earlier, they might have very well ended up together. Another is a lot of the qualities that are present in him early on — he's smart, very driven, idealistic and not without compassion — might have made him a better hero than Captain Hammer, but combined with his flaws, send him hurtling him toward supervillainy. 

I admit I find it very hard not to feel for Billy; I happen to be geeky, introverted, insecure and cripplingly shy. On my good days I'm a little withdrawn; on my bad I am so scared of other people I can barely function in the world. This particular combination of flaws sometimes results in my doing really stupid stuff for an intelligent person who knows better, but usually the only one hurt is me. 

I guess what really undoes him is his very low EQ — emotional intelligence, as opposed to intellectual intelligence.