That's the ideal solution, but not the only solution.
So there should be no land ownership
There already isn't, in absolute terms. A government can reposses any piece of land within its territory (maybe with the exception of embassies) at its own discretion.
Another simple solution is that the taxation on any land should be proportional to its market value deduced from a "usefulness" score, i.e. tilled land used for farming is very useful, therefore shouldn't have increased taxes. Empty houses aren't useful at all, therefore high taxes are justified. This is a developed application of Land Value Taxation.
Even if you argue for the ownership of a house, the land it sits on is ultimately owned by the state, so I don't think that's a very productive topic...
Not necessarily for free (although, as I stated, that would be ideal), but certainly not for profit.
That would be incentivised, yes.