"Give people a choice, and they'll only pay for what benefits them personally." This isn't actually true, people pay to charities all the time. We used to have a robust system of mutual aid societies before the government squashed them. And if someone chooses to only pay for what benefits the personally, that's their right.
"People won't pay for schools to educate other people's children, or schools that teach a curriculum with which they disagree." People donate to schools and set up scholarships for the poor. But we expect parents to pay for the needs of their children for everything else, including daycare, feed, housing, etc. And if a parent can't afford the property taxes they will be made homeless. And why should someone be forced to pay for a curriculum they disagree with?
"They won't pay for libraries whose books they don't read" People set up little free libraries, no reason it couldn't be set up in a larger scale, all paid for voluntarily without taking people's homes if they don't pay. I would say housing is more of a need than a library. And everything is practically free online already. But a library could be a service built into your mutual aid society along with the school for your kids.
"or for parks, because homeless people hang out there." We pay a few bucks every time we go to the arboretum, and if we wanted to we could pay a yearly fee to become members. Our HOA pays for the local park. No reason to steal people's houses to pay for a park, creating homeless people. Why am I paying so much money in taxes if society isn't even going to take care of homeless people? I would want my tax dollars to go to that before a park or a library!
"People will just buy smoke detectors and not fund the fire department." Well, I hope we all have fire detectors. There's no reason that fire protection can't be bundled in with your homeowner's insurance, which is required by your mortgage holder. The city has no liability if the house burns down and the fire department fails to save it. Let the homeowner's insurance, which carries the liability, hire the fire fighters.
"People won't fund the police, they'll just buy insurance or keep a gun under their pillow." The Parkland school shooting victims would tell you that the cops didn't help them, and the court ruled that the police had no obligation to protect those children, and it was fine for them to wait outside while they knew children were being shot. If you want to pay for police protection that's fine, but if someone wants to hire a private security firm, (which could be bundled in with homeowner's insurance like fire protection), or own a gun, or organize a local gun club, or whatever, that's fine. It would keep the local police department honest if they knew that if people didn't like their service they would stop paying.
"They won't pay to fix the roads unless they're inconvenienced by a pothole." In some places the government is terrible at fixing potholes and Domino's Pizza is doing it. But this should be paid for by the gas tax as I explained in detail in a different comment to someone else. If you choose not to drive, and choose not to pay for the roads, you shouldn't have your house taken, you just shouldn't be allowed to drive on the roads.
"And welfare and other social programs would just vanish altogether." Well this just isn't true at all. We used to have mutual aid societies that worked really well. But then the government put regulations on them and started government programs that did many of the same things like social security, medicare, medicaid, unemployment insurance, etc. We still have insurance for many things the government doesn't cover like life insurance, health insurance, disability insurance, etc. And if people do find themselves without a mutual aid society, or insurance to help them when someone thing happens there are people willing to help. We saw how people stepped up to work the food banks during the lock-down and there was a lot of need. Food stamps doesn't pay for much and there was still need and charity stepped in.
"Most people would refuse to pay any taxes at all to a government run by a political party they didn't vote for." That sounds great to me. People wouldn't have to fight anymore. I have neighbors that are Catholic, Muslim, Buddhist, Protestant, Jewish, Mormon, and we don't fight about it. We can all go to our place of worship, tithe or give money to whatever organization we want, follow whatever rules, etc. But when it comes to government policy, like what will the taught in the schools, then it becomes a fight. We had a school board meeting be done virtually last minute because the school board claimed they were afraid for their safety because so many angry parents were showing up. If we are getting to the point where we can't even have a school board meeting without fear of violence, it's time to try freedom.
"There's a reason taxes are collected at the point of a gun - you can't trust public altruism to fund a modern state." Yes, the reason is because this is the way the King of England did it, so we did it, and we're still doing it, even though it's not right. It's not like anyone has seriously considered it, tried it, found it lacking and decided to go back to the old way. That's why these ideas sound so foreign to you and you have so many questions. Few have ever seriously considered this before.