I think you are vastly oversimplifying things. For starters, who is going to organize this? If you don’t have food or shelter, your only focus for the day is find food and a relatively safe place to sleep at night.
But, let’s say that they did organize. We know what the outcome would be: the police would show up, beat the shit out of them, jail them, and throw away what few possessions they have left. And most people’s reaction to that would be “I’m glad the police finally cleaned up our streets” because, whether they want to admit it or not, most people hate the poor, and especially hate the unhoused and just want them to disappear. I can say that with confidence because that’s what happens in major cities when the unhoused do anything, every. time. Those who have been suffering for a while have had the spirit beaten out of them, and the recently unhoused quickly learn to follow suit if they want to stay alive and have any hope of improving their lives because if you have any criminal record whatsoever, you immediately become unhirable to 90% of businesses. Creating problems for the system is a way to guarantee you will remain unhoused for the rest of whatever life you have left after.