Them staying in the sidewalk is free. Or the cost is so indirect that nobody is responsible for it.
Facilities like asylums and jails are super costly though. And extra expensive to operate if you don't want to treat the inmates as cattle.
The cost is not measured in dollars, but rather in the pollution of the pubic space. People feel less safe and more bothered. Stores nearby get less business, and suffer more theft. Passerbys get accosted.
> Them staying in the sidewalk is free.
Disagree. When the tax-paying public doesn't feel safe around the people living on the sidewalk, they move and take their tax money with them. That means less money for services, roads, education... everything taxes pay for.
That's the cost.
I'll add that treating the inmates like cattle is actually the most expensive option of all in the long term. The USA has one of the highest incarceration rates in the world largely due to high recidivism due to the system not providing proper rehabilitation.
So it's costing the USA 65k/yr per inmate on average right now with the 5th highest incarceration rate in the world. The 4 countries above it are not nice places to live contrary to the thought that locking even more people up would make the USA just like the other western nations of the world.
No other country is as stupid as the USA when it comes to homeless. They don't spend a lifetime $65k/yr repeatedly locking up such people. Instead they spend a fraction (when amortised over a lifetime of jail costs) on rehabilitation and public health programs.