Yea. It's not very hard - if you want something responsive, you have a limited amount of time between when you read input and when you present something on screen.
This delta can be greater than the rate at which you present images. For example, most game engines take 30ms to read input and simulate on a thread, then take 30ms to renders on another thread while the next frame is simulated. This means that they present something every 30ms, but the delay between input and rendering is 60ms. This delay can be up to 100ms and not be noticed by players.
A 100ms delay is extremely noticeable, especially for faster paced games. That's 6 frames at 60FPS, or 3 at 30. While you may get away with that on 4X games, no FPS will ever get to more than 50ms input lag, because it seriously becomes unpleasant to play.
I might be misunderstanding what you're saying here, but from what you've said it sounds like the game would run at ~30fps, whereas many games are designed ideally to run at 60fps, which would allow only ~16ms to take input and simulate?
This delta can be greater than the rate at which you present images. For example, most game engines take 30ms to read input and simulate on a thread, then take 30ms to renders on another thread while the next frame is simulated. This means that they present something every 30ms, but the delay between input and rendering is 60ms. This delay can be up to 100ms and not be noticed by players.