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Not really. You can develop deterministic physics engines. It was one of the required projects on my university to create simple deterministic engine. It is just not needed for most applications, especially games.
so the real issue may have more to do with the fact that unity does not use a fixed clock rate, but instead does what 99% of game engines do, which is calculate the time spent on the last frame and adjust the time step of the world process accordingly. meaning *any* slowdown, or speedup, in the game engine will affect how your physics engine works. and since the game engine is dependent on the OS to get many things done, any time the OS can't deliver a resource in exactly the same time it did before, the engine speed will be affected, and your physics will be affected too.
so whether you use an input recorder or not is moot... unless your engine runs physics in a fixed timestep you won't get consistent physics results.
So if I cap the framerate of GOI to 20fps (using a means that would in reality render speedruns fake, and assuming it will never drop below 20fps on high end systems), a TAS is completely plausible?
If you really want this your best bet is to ask Unity to create a developer option for setting a fixed update cycle on the physics simulation, then ask bennett to expose this option to the user via the game's settings window.