I wonder if a system where keeping a patent active requires paying an exponentially increasing annual fee would help. So anyone could file a patent for say $1,0

I wonder if a system where keeping a patent active requires paying an exponentially increasing annual fee would help. So anyone could file a patent for say $1,000 in the first year, but then it would cost $2,000, $4,000, $8,000, etc. to keep it active in subsequent years. That way, it would be financially infeasible for even the largest companies to hoard patents for years, but an individual inventor could start small and pay the fees as their business grows.