I'm trying to understand: are you saying landlords should be able to not pay property taxes on the current value, not get their property seized by the state if they don't pay property taxes, collect market rate rents from tenants, and also keep all of the profit from property value gains once they sell?
But ignoring that absurdity - property taxes are usually 2% of the property value. So you'd need to what... Not pay any property tax at all for 100+ years for that scenario to play out?
But let's say we allowed that to happen, and we're somehow sympathetic to that owner. You still don't evict anyone over property taxes. The next buyer will just have to work it out. See Detroit and its $1 homes with $20k in back taxes.
I guess the problem here is I don't see housing as something anyone should expect a guaranteed profit from. I view it just like anything else - there's real risk, and if you're going to privatize the profit, you damn sure better privatize the risk, too.
I'm very much for private ownership of property, not sure why you would think otherwise. All I've said is to do what just about every other state does: if your property is worth $200k, you pay $2k that year in property taxes. If it's worth $2 million, you pay $20k. This isn't hard, and it isn't controversial.
Edit: just to appeal to authority: every single legitimate economist agrees with me on this as well.