"clean up" and "mature" are umbrella terms that include a lot of different processes!
Obviously, if you crash too soon, that will stop fermentation, which could lead to an underattenuated beer if there is still any last few percent of slow fermentation going on at the time.
Also, crashing too soon may prevent the yeast from cleaning up any diacetyl left over from the main fermentation. Whether that is a problem depends on what yeast you used (ie. whether you're likely to have too much diacetyl in the first place) and also your fermentation temperature.