I manage a shelter for women and children, it is not at all like you describe. Almost no one ends up homeless because that's truly the life they want. A lack of accessibility to mental health services is probably the biggest issue; but also domestic violence, and a lack of accessibility to resources like healthcare, food security, and childcare are a huge contributing factors.

Are all of my clients perfect? Nope. Do I have my days when their behavior frustrates me? Of course. But I still feel for them and want to help them because it's likely their cognitive functioning and major systemic failures that got them there. Basically what I'm saying is that your lack of empathy is more of a reflection on you than the homeless people you've encountered.