Non-electrlytics are also more expensive than electrolytics, especially for large capacitances. THis is pretty much the reason why they are used where they are, rather than some other kind of capacitor...it's pretty much their only advantage.
It doesn't need to be electrolytic. The value depends upon the lowest frequency to be bypassed. The reactance of the capacitor is generally 1/10 the resistance of the emitter resistor, so the value of the capacitor depends upon the frequency.