Extrapolation isnt worth the chance of misprediction if it's a player movement based game.
The 'input latency' introduced by interpolating between frames is far different than typical 'input latency'. It's less than a single frame, and the game still renders movement at the same frame, just less movement. Most 'input latency' tests only test for _any_ movement, so those kinds of tests would detect 0 difference between 'interpolation', 'extrapolation' and 'render the exact game state'.
I'm a fast paced gamer, and I make fast paced games, I've never once 'felt' the input latency from interpolating the players position between simulation frames.
Using two frames to interpolate at render time is adding one frame of latency.
It is possible to do it on a single frame, extrapolating instead of interpolating, but you have to use a simple but uncommon trick to make it robust.
The latency gain is not a full frame but some sizeable fraction of a frame, I think it is worth it for some games.