If something is in L3 it is better for CPU "utilization" than stalling and reaching out to RAM. I guess there are eventually diminishing returns with too much cache, but...
Any mid+ CPU will easily pump out 240FPS on Counterstrike or Valorant.
But I've heard of triple buffering setups where you're displaying the current frame, and once you have a complete next frame, you can repeatedly render into the second next frame, but the next frame isn't swapped. In that case, it's hard to argue for any gain, since your next frame is way old when it's swapped to current.
Some rendering systems will do double buffering where the render is scheduled to start just in time to finish with a small margin before vBlank. If you've got that tuned just so, that's almost the same latency benefit as running unlocked, but if rendering takes too long you have a stutter.