I'm not totally convinced it's much more than trying to assuage our guilt for not being homeless. Don't get me wrong, it's a lovely idea, but I'm not convinced in practice.
I agree with the poster about people finding it humiliating to ask. Extra humiliating if the cafe hasn't had any paid for. Imagine plucking up the courage to go in and ask, and being told they didn't have any that day.
and having to go out feeling everyone heard you and saw you turned away.
Also, this is going to sound horrible, but I do know some people that would happily go and ask for one. They would not be in the category that need them, they could pay for their own if they had to. But if they could get it for free, then they would. I suspect if it really took off, then the people in that category would increase. They wouldn't see it as humiliating-they'd see it as getting one over and probably laugh about it.
I also wonder whether charities, like shelter, would actually miss out too. People would think "instead of paying £5 a month, I'll just get a suspended coffee". Or "shelter doesn't need it, I've seen those people getting suspended coffees and they look fine..."
And a coffee is great for short term, but long term is very much needed, so if the charities that look out for long term solutions are missing out, ultimately more people will suffer further hardships.