I guess if you were homeless it might be worth £9 a day to have somewhere warm and indoors to stay, but the free entry museums, art galleries and libraries don't seem to get full of homeless people.
I have heard reports of 'pay what you like' restaurants getting filled up with homeless people, so I can see where you're coming from.
That's really funny. Who would have thought there were more people who like eating for cheap than people who like paying for other people to eat for cheap?
Security Guards.
Also, dress codes are most likely in effect.
But when it comes down to it... they're actually $12/meal minimum throughout the week, and on wednesdays (most B&M business' slowest day in north america at least) they offer something like 50 meals which are "pay what you want" and once they're out of food, they're out.
In other words, "pay what you want" restaurants don't technically exist. Not in the long run. They're more of a marketing gimmick if you ask me.
The free rider problem is a very real thing: http://en.wikipedia.org/wiki/Free_rider_problem