Which is why we need a world where people are constantly being forced to move and never allowed to ever stop moving, for fear that they may some day stop and think.

To add another layer: allowing homelessness is one of the most widespread and visible acts of violence perpetrated by the state, supported by the market, and accepted-- or at least tolerated-- by most of the public. I wonder if institutions don't address it because scares people into obedience.

Reflect on the focus of violence in stories about slavery. Hypothetically, without violence, slavery is still awful: robbing a human of their autonomy, spending their lives bettering the lot of those in power rather than their own. But we focus on the violence, not only because of the obvious, visible horror, but because you can't rob someone of their autonomy without violence.

When it comes to homelessness, the violent act is not only inaction: failing to address risks and pitfalls, or add safety nets (focusing on growth, instead), but also what your original post is about: removing public facilities, forcing people to play the line-go-up game in order to have nice things, lest they have a string of bad luck and end up on the street, exposed to the elements.

The state and market didn't cause the blizzard that may kill unhoused people, but they did nothing to try to get them out of its path. Isn't that the purpose of these institutions? Yet homelessness is everywhere and it makes being unemployed all the more terrifying-- to be that much closer to the streets. "Better to take what you can get," participate in an unjust market or it could be you.

Far more often than not, even bloody revolutions do not achieve their goals, or lead to merely cosmetic and/ or short-lived changes. E.g. Kent Gang Deng investigated 269 major peasant rebellions over 2106 years of Chinese history. Guess how many of these actually rewrote history in any way, shape or form.
Recently, I've been reading several interesting pieces on the "Occupy" movement, the related G20 and other protests in the Western world, dating back as far as the 1960s. The bottom line being: asking nicely for some minimum demands that even conservative politicians can get behind, like capping CEOs' wages, will not get the job done. In fact, some of the powers that be can use it for their internal power struggles and to show it off as a sort of legitimization folklore. "See how democratic we are? We even have protesters in little tents! Don't worry, they aren't hurting anyone."
All hope is not lost, though, if new protest modalities can be found.