A land value tax is an absolute must, same goes for the rest of what you'll said.
But it isn't a magic wand. The culture still needs to catch up, as many unfortunately still see being a landlord as an actual valid job. And even under a land value tax system landlords could still exist. Nowhere near as exploitative, but they'd still exist.
The concept of a free market relies on a hidden assumption that the choice between products is a free and easy one with a low switching cost. Housing is none of those things. It takes time, money, energy, you need to be able bodied or able to afford movers. If you have a job you might be stuck in a given area. People are heavily de-incentivized from moving, and that's always going to be the case no matter how housing is made and distributed.
As a result, landlords will always have enough room to exist in a housing market, even if it is a land value tax system. So if by "LVT would fix this" you mean stop landlords from existing, LVT is only a stepping stone.
A VERY good stepping stone, but only a stepping stone.
Then you don't understand fascism.
People suggest that all the time.