During training you're trying to find paths to success, and reinforcing those.

There is going to be some minimum length path (assuming the model is generating some semblance of real reasoning), but more long ones given the possibilities for less optimal solves and backtracking after errors, so it stands to reason that if you think longer during training you'll find more paths to success.

At inference time you are hoping to follow one of the reasoning paths discovered during training. You need to generate enough tokens to follow the path (or one of the paths), but continuing to think past this point can only be detrimental - if you are lucky the model will realize the error and circle back, but if you are unlucky it will snatch defeat from the jaws of victory and wander off to who knows where.

There was a story recently linked here about one model "editing the weights" of another and thereby improving it's math performance, which was exactly about this - the need to stop generating at inference time at the right point.

IMO LLM's RL acquired reasoning, even if it gets the job done, sometimes spectacularly (math, coding successes), is really a very dumb cargo-cult process. At inference time the model is just trying to copy what it "saw" at training, without actually understanding it, which may even include duplicating errors and subsequent backtracking that had lead to success during training.