I want to know if a washer that does 2 gpm @ 2000 psi has only half the
"cleaning power" as one that can do 4 gpm at 4000 psi (ie does the
cleaning power scale linearly with these numbers, or geometrically or
exponentially).

The second is 4 times better. Anything can give you pressure.
Even your grease gun can give you 10,000psi. The GPM rating
far outweighs the pressure rating.