not necessarily. Due to adaptive sync and render thread/game thread can become somewhat doing their stuff in parallel, modern engine can reduce the old fixed 3 frame input lag into mostly 2 frames and with some good scheduling 1 frame input lag is possible for 30fps.(the higher the frame rate the more impossible to achieve 1 frame input lag, like even if your game is just moving a cube in empty space, above certain frame rate it becomes not possible to keep 1 frame input lag due to engine overheads.(note here we do not consider display input lag, just your input action and then later gpu draws the update. )

You can see that’s a very big improvement for 30fps based games. ie. old engine with fixed 3 frames lag, 60fps is about 50ms, where if it’s 30fps but with 2 frames input lag it’s 66.6ms, and it’s not a lot different. So it becomes sort of standard for raytracing enabled game to target 30fps, or like ratchet and clank where they have modes that targets 40fps as a compromise.(that needs a 120hz monitor as support), oh, why 40fps?? if you do the number, 40fps with 2 frames input lag is 50ms, is this number familiar? yep, it’s the same input lag as old engine where 60fps but have fixed 3 frames lag.