For most modern gaming monitors, this isn't a huge deal. Cap your game at 140 FPS on a 144hz display and it will feel as snappy as it probably would have uncapped. Though if you have a lower end (or ultra high resolution) display that caps out at something much lower, like 60, then I can definitely see how leaving it uncapped with VRR disabled would feel a lot snappier.
Early Freesync-branded displays could also be a bit of a crapshoot for a variety of reasons, but this has gotten much better in the last 5-6 years.
That sounds very weird to me, why would that be the case?
(also FWIW i'm using Linux so a system-wide cap isn't exactly possible, though at least with games i can simply run them via mangohud)
My understanding of why this causes a problem is that the CPU starts running ahead of the GPU, and queues up frames to be rendered. So it shouldn't be a problem with games that support Nvidia Reflex or some other feature to limit pre-rendered frames.
I have a Freesync display and a compatible GPU and i can feel the difference between no vsync and freesync. There is a slight lag there, if you cannot feel it do not assume that others cannot too (some people even seem to not be able to feel a difference between having vsync on and off or having a compositor or not enable - nowadays really only possible on Linux but in the past you could also do it with WinVista/Win7 and in Win8 with hacks like the one linked - which is mind boggling to me).
Of course the input lag depends on the game and how you play it. First person games with raw input, 1:1 mapping of the input (i.e. no filtering whatsoever) and little to no frame queuing (some engines run 1-2 frames "behind" the game state and if you add things like triple buffering you end up with extra lag) are the best to notice this whereas third person games played with a gamepad (where you have only indirect control of the camera - you control the camera's rotation speed, not the camera directly) are way harder to notice, as are games where you mainly use the mouse to click where to go (especially if the game uses a hardware cursor instead of rendering the cursor itself as part of the game UI).
Also high refresh rate monitors make it slightly easier to overlook the lag (though it still is possible to tell - mine is a 165Hz monitor after all and i can still notice, it just doesn't annoy me as much as on a 60Hz monitor).