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If it is tied to frame rate, then a set of inputs results in a predictable set of outputs.
If not tied to frame rate, those same inputs have to be reproduced with the exact same time delay, which is almost impossible to do.
Sure, sub-millisecond time differences might not always lead to a different output. But it might.
Now, when is this determinism useful?
TAS (tool assisted Speedrun). You can't tell the game: on frame 83740 press the A button. Given a list of inputs with their exact frames will always lead to the same Speedrun.
Testing. You can use methods just like TAS to test your game.
Reproducing bugs. If you record the game state and inputs of a player before the game crashes, you can reproduce the bug, which means that it will be a lot easier to find the cause and fix it.
Replays. Games like LoL, starcraft, clash of clans have a way to see replays of gameplay moments. If you save a video for each one of those, the storage costs will be prohibitively expensive. What they do instead is record every single action and save that. And when replaying, they run a simulation of the game with those recorded inputs. If the replaying is not deterministic, bugs may appear in the replay. For example if an attack that missed by one pixel in the game was inputted a millisecond earlier in the replay, it may hit instead. So it would not be a faithful replay. This is also why you can't just "jump to minute 12 of the replay", you can only run the simulation really fast until you get to minute 12.
I'm not a game developer so I don't know if it is used for testing or reproducing bugs or replays. But I know it is used in TAS.
Of course, for this to be possible you also need your RNG function to be deterministic (in TAS). In the rest of scenarios you can just record what results the RNG gave and reproduce them.
You can still absolutely have deterministic inputs without tying the inputs to the frame rendering. Just have a separate thread for the game logic that runs at regular intervals.
Just look at Minecraft. 20 game ticks per second during which all the game logic runs. But the game absolutely ain't limited to 20fps.
Yeah, you can still have a "tick rate" that is different from the rendering rate. Factorio also does this.
I don't think OP is asking about that case though.