Why does a crossover make a woofer and a tweeter sound better than just sending the full audio spectrum to both speakers?
The crossover sends only bass tones to the woofer, and only
treble tones to the tweeter. The woofer does not have to try and
reproduce high tones accurately - which it cannot (they would be
muffled), and the tweeter does not have to try and reproduce bass
tones (which it cannot at all.) The sound is much more even and
balanced.