One reason to separate low bass and midrange frequencies is so that heavy bass information does not ruin midrange info if they are playing on the same driver. Soft cone drivers bend under the heavy acceleration at the top and bottom of excursion. But rigid cones may ring at higher freqs. Very few large woofers can pull this off 20-2000 without some problems. Ports are usually employed to be the third driver but they're not perfect either.
Another reason to separate bass and mid is to optimize the power response, so that off-axis frequency response is as uniform as on axis response. All drivers beam as frequency increases, so when a beaming woofer crosses to a dome tweeter that is playing omnidirectional there is a power mismatch in the radiated acoustic energy. On axis they are same SPL, but off axis they are not, so the power response is messed. Off axis sound is what creates most of the echos in your room, which make up a large part of what you hear. Good power response is necessary for a great sounding speaker. A true midrange can connect a bass and tweeter together gracefully, and add a lot of headroom and dynamics.
The additional driver and crossover circuit will add cost and some phase error, but will reduce distortion in other ways that many people prefer. Some people hear the phase shift and would rather avoid that, but they usually give up something in exchange.