Capacitor-less amps

Yes.

It is also possible to make a crossover for the speaker where the tweeter has no capacitor in series with it. It uses an inductor across the tweeter. The drawback is that such a crossover wastes a lot of power in a resistor needed to avoid a short circuit on the amp at low frequency.

All amplifiers have capacitors. I suppose theoretically one could be run off humongous batteries, but converting AC to DC will require capacitors. Many companies tout having no capacitors in the signal path. This requires an extra level of care as speakers will detonate if significant DC is present on the output. There are numerous design techniques to eliminate the DC without caps.

Vecteur, YBA and REDesigns all make amps with no Caps in the signal path.

They are all very natural sounding amps and quite stunning in the right system. This is no accident.

SimAudio claims that their amps have no caps in the signal path. I believe that they do put caps in the power supply, though.