Interesting note about your professor. It's been a number of years since I did analog audio circuit design, but I remember one rule of thumb from the articles I read in the "hobbyist" DIY audio publications: avoid tantalums in your signal path.

I can't find the articles I read in the past, but a quick web search does yield information. One in particular seemed to cut right to the chase:

"I'll be dogmatic about this: tantalum capacitors _stink _for audio use: they should never be used in any signal-carrying circuit. They sound tubby in the bass, harsh and gritty in the top end, and
compressed in their dynamics—mirroring their poor engineering performance in such factors as dielectric absorption." -- from http://www.geocities.com/Area51/Nebula/3736/improve_audio.txt

This is, of course, far from a known trustworthy source, but it does confirm what I remember reading and researching at the time.

Back to your point, though: I agree that any capacitors used in a typical reasonable quality piece of consumer gear, running well within tolerances (don't forget, we're talking about signal levels nominally of a few volts here), shouldn't be changing dramatically, noticably, or probably even measurably early on in their life.