I would flag that we’re getting into “prove a negative” territory here: the goalpost is that we need to prove empirically that patents achieve the desired outcome. If the scenario you describe accounts for all game-theory/incentive/complex-adaptive-system universes, we should see this reflected in the data.
When it comes to pharmaceuticals, they looked into Italy and Switzerland who switched to a patent system in 1978 (and I believe Portugal in the 1990s). They looked at the growth curves of things like # of inventions, total factor productivity, percentage R&D spending, and the conclusion was that there was no statistically significant change in trajectory that would suggest the introduction of the patents had any positive effects. (Edit: they accounted for domestic/international + US filings before/after as well).