Capacitor in parallel with main driver

An inductor in series with a driver acts as a 1st order low pass filter. Add a capacitor in parallel (of the right value) and it becomes a 2nd order lp filter.

What, if anything, is the effect of having only the capacitor in parallel?
 
The capacitor has a reactance (impedance, or sort of resistance) that falls with frequency. However the ideal amplifier is a very low impedance voltage source, at least to a point. So as the impedance of the capacitor falls with rising frequency, the amplifier simply supplies more current to maintain its idealised voltage output level, to the point that it starts to current limit. All in all, that's not a desirable scenario.