Why would the state want it? Wouldn't they have to pay the same tax as other people?

Pay tax to whom? The state?

If the state owns the property, they lose the opportunity cost of taxes paid by a private owner. So, they're heavily incentivized to return it to private ownership as soon as possible... Or to consolidate several such properties into something that is sellable, or to repurpose the property into something people need, like more housing.