The difference between owning and renting is already a matter of degrees, particularly once you add rent control, mortgages, condos and HOAs into the mix. The renter already has the right to deprive the owner of the property value increase, this is just creating a legal framework to give it back for cash. I'm imagining it would only be part of the value of increase in rent over the rent-control limit, not all of it.

It would increase market price rents modestly, as you're essentially depriving landlords of the power to shake off bad tenants by finding rent control loopholes or waiting them out, but you could offset that by creating a process for voluntary tenant buyouts.

Buyouts are currently very difficult to carry out legally even if the tenant wants to leave and the landlord would rather replace them with someone paying more, leaving the two parties stuck together in an unhappy marriage as an unintended side effect of the way the laws work.

In response to your edit: Of course you'd pay for them, new rentals are market-priced (then locked into rent control until that tenant leaves), aren't they? It's got one-sided risk like any option but those aren't hard to price. It's in everyone's interest to increase the future value of the rental unit.