Output impedance of the error amplifier driving the pass element increases with frequency for the reason you identify but this does not have to be the case. A parallel capacitor could be added to ground and appropriate frequency compensation adjustments made if necessary (1) producing a "regulated" capacitance multiplier. In the primitive form, this could be the old ubiquitous zener series regulator in the form of a capacitance multiplier with one added zener diode.
Yup. Of course, as history has shown, designers are loathe to touch anything that needs extra capacitors, let alone capacitors that have confusing, complicated requirements, like... "compensation".
I would say the other reason this is rare, is more because you need a big stinking cap to do it, in semiconductor terms. So you'd be asking for another pin (ain't gonna happen on a TO-220 device, say), plus inviting that opportunity for the user to get it wrong. But yeah, not having all that much benefit is another drawback.
On that note, there are a few LDOs out there, targeted for RF applications, with impressive PSRR up to and beyond 1MHz (where LC filtering is quite economical to take over at). But they aren't cheap.
More interesting I think are the capacitance multipliers which used a shunt element instead of a series element. The audio guys like these but I am unconvinced.
Mmmh, shunt is fundamentally limited by the gain of the device. Say you do a BJT shunt amp, collector to supply, emitter to ground, with some base bias, and a coupling cap from supply to base. This has exactly the impedance 1/Gm. So, for 10mA bias, say, only 2.5 ohms. A small electrolytic is better, and by a MHz say, a modest ceramic cap more than dominates.
Whereas a pass device is limited by Early effect and Ccb vs. Cce, which can probably give a much higher ratio.
I suppose you could combine both, so that the capacitor being multiplied, is multiplied twice, in a sense. You could supply the whole thing from a gyrator or something, so that the source impedance is higher than an equivalent resistor, giving more stopband width and depth for the same bias current. Doing this for just the base RC filter network, you wouldn't be improving the main pass transistor at all, but you could improve its filtering with respect to bias current, economizing it a little.
Tim