The reason for using a capacitor is to prevent low frequencies reaching the tweeter. Low frequencies will affect the output quality of the tweeter at best and can easily damage it.
Bass speakers are frequently driven with a coil which is (approximately) the opposite of a capacitor in that they block high frequencies and pass low frequencies. However, the presence of high frequencies in a bass speaker tend not to cause any noticeable issues. The speaker itself is a coil so it tends to attenuate the high frequency currents without additional coils. Furthermore, the high frequencies won't be heard because the speaker simply doesn't move at those frequencies.
The science of crossovers for speakers is complex. To get the right crossover for a high and low frequency driver takes a significant amount of calculation and the speakers themselves have an effect of the characteristics. The advice above is very general and the results of not using a crossover are unpredictable.
If possible, it is generally more effective to use a line level crossover. This will process the signal and separate it to two or three signals. It does it without relying on the characteristics of the speakers so it provides a very accurate crossover. However, as well as the cost of the line level crossover, each speaker needs its own amplifier channel so costs can rise significantly.
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