Are there any applications where it’s beneficial to have the drive ratio be as exact as possible? (Other than machining).
If you mean ‘as close as possible to a specific ratio’, land speed record or salt flats cars. Ideally, you want the car to be drag-limited to the speed that corresponds to its peak power rpm. But on a run of finite length you probably want a slightly shorter ratio.
Given that maximum power occurs at some specific rpm, and that the power curve is likely to be rather peaky for this endeavor, if you’re geared such that the engine rpm required to hit the speed permitted by the available power is either higher or lower than the rpm where peak power is developed, you won’t make it to that speed. Geared too tall and you become drag-limited before you get to your power peak. Geared a little too short and you pass through the peak power rpm at a lower speed than what the power would ultimately support and become drag-limited on the high rpm side of the power peak, as the power is dropping off.
Above is a snippet.