> a lockstep solution which only considers inputs
Nothing stops you from adding a PRNG seed parameter to initialize your deterministic game engine.
Nothing stops you from adding a PRNG seed parameter to initialize your deterministic game engine.
But if you're running a multiplayer game with random elements and aren't colluding, you don't have to let a malicious party set the RNG seed to whatever they like just because you agree on it at game start. There's any number of simple cryptographic protocols that allow each peer to contribute equally to the RNG state based on having a separate commitment phase. And it's a lot easier to run a quick cryptographic setup than it is to have constant input-driven adjustment.