Many inexpensive receivers have limited power supplies and simply cannot drive "full range" average speakers to a loud volume in a large room. If you try, they'll "clip", causing distortion and possibly damaging the tweeters in the speakers.
A crossover which diverts the low frequencies to a subwoofer reduces the need for the receiver to provide the power needed to drive low frequencies, making more power available for the upper frequencies, thus reducing the likelihood of clipping.
Of course, most inexpensive speakers simply are not full-range and you need to specify a relatively high crossover frequency to divert the lower frequencies to the subwoofer in order get any kind of reasonable sound.