> I have thought of a scheme where the first couple of years of IP are free and after that heavily progressively taxed over time ( e.g 1000 usd on third year and doubling each year after that. Once the ip holder does not pay the tax, IP becomes automatically public domain.

It's not free at the beginning, and the fees are less than you suggest, but that's mostly what we do have: https://en.wikipedia.org/wiki/Maintenance_fee_(patent)