As a psychologist & disability studies academic, working in a department of mental health, in a UK university, I have a particular view on this sort of photography, and maybe a slightly different 'take' on it than some.
Here in the UK, we don't worry overly about profit motive in healthcare, though our current chimera/coalition government seem set on privatising the hell out of the NHS. We've seen the closure of long-stay institutions & implementation of care in the community, and the variable quality of it. Our streets & prisons are replete with individuals struggling with mental ill-health, and many of those on the streets are ex-servicemen. The latter issue is ironic, not least given the alleged concern politicians have for our ex-military & the current outpouring of (justified) outrage at the actions of some journalists in hacking the phones of families of soldiers & marines killed in Iraq & Afghanistan. Frankly, hacking phones is small beer compared to the lack of care & support for men mentally scarred by experiences in war zones. Add in the numbers homeless & on the streets for other reasons, begging, busking or selling the Big Issue, many of whom have mental health issues too, and it is a problem that should cause far more pause for thought than it seems to do.
Personally, I have no problem with photographs of people, and we should remember that homeless & mentally ill people are still people first & foremost, and so photographing them shouldn't be off the agenda. But at the same time, issues of consent & the like, impact on the ethic that underpins practice, including photographic practice. I think it worth asking ourselves question of the kind, "Why am I photographing this person?" & thinking critically about it. What purpose does it serve? Personal interest? 'Hey! Look at this wonderful portrait I took of some poor down-and-out' hardly constitutes an ethical engagement with the subject. But there might well be considerable value in such photographs, if they are used in some campaigning way to raise public & other awareness.
Fair exchange is no robbery, but I worked with a woman who was selling her body for cigarrettes whilst sleeping in the local night shelter; sex for a half-smoked Silk Cut is abuse. But what about payment for taking a photograph? Is a cup of tea enough? Well, most people would probably let you take their photo for nothing, if you asked nicely, or even if you didn't. Sitting & chatting with someone, buying them a drink, giving them a copy of the photo - assuaging own feelings of having intruded, or sharing some common humanity & displaying a caring attitude? Some might say that we should do the latter anyway, without expecting anything in return. But then again, interdependence is no bad thing, and some people on the streets might like the thought that they've somehow earned something, or given something. Social transactions take many forms, but many people on the streets find themselves constant recipients of handouts & charity, and trading something might well give a vital feeling of self-respect.
These aren't easy black & white issues, even if the photos usually are.