No, but they can just keep buying up a large share of the houses you build. You probably can keeping building to a point where foreign investors begin to lose

No, but they can just keep buying up a large share of the houses you build. You probably can keeping building to a point where foreign investors begin to lose interest — but Americans do not generally like very dense housing, so this sort of becomes throwing out the baby with the bathwater. You're potentially making housing more affordable by turning the neighborhood into a ghetto.