Oh please... I will probably only cause anger in you but i can't help correct you, even if do it clumsily.
"We have air conditioning everywhere. We have freely available water. Everyone can have a phone, but not just a phone, a cellphone. We have freely available internet." - these obviously cost money... what are you talking about?
"At what point are these people choosing poverty, and if that is the case why should we care?" - at no point does anyone chose poverty; you don't have to care. Choosing or not to do is what separates one from being selfish or selfless, that's it. If you're rich enough that there is absolutely no possibility for you to ever become poor because of a drama in your life you definetly don't have to, but if you're not that rich, you could think of how you'd need people to care if you did become poor yourself.
"However the vast majority of these are people with mental problems who are high-enough functioning to not be compelled into assistance, who then go out and choose this lifestyle." - Yes, right. All these homeless living in constant fear and hunger just chose that confortable life style. Tonight i'll go rest in my sofa in front of the TV but really, deep inside me, what I want is to sleep in the cold and filth of an underbridge, constantly waking up at any noise, scared of being aggressed. That's the life. Seriously, if people have mental issues they need to be taken care of by psychiatrists and possibly mental institutions, not just left to rot in the streets.
If you're rich and don't want to care about the poor, fine. Other less selfish people will do it. But don't invent such lame excuses to not care about them and accept the fact that you're selfish.