You have the right idea, but the wrong numbers. Terribly, terribly wrong numbers, it's quite clear you're making those numbers up. No filter for an audio ADC would ever have a cutoff as low as 2.2 kHz, not even if it were for a telephone. (You have a strong signal theory background? No offense, but really?)

When you use a 44.1 kHz sampling frequency, any frequency above 22.05 kHz will be "aliased" and recorded as a lower frequency. This sounds incredibly nasty, like the sounds you'd get out of a broken Commodore 64. So you have to remove frequencies above 22.05 kHz in order to get a clean recording. But human ears can hear up to 20 kHz or so depending on age (e.g., NTSC TVs with cathode ray tubes have a 15 kHz horizontal refresh which drives me nuts, but my parents can't hear it at all).

The trick then, is to design a filter that will let the 20 Hz - 20 kHz band through while stopping everything above 22.05 kHz. We call 20 Hz-20 kHz the "pass band" and 22.05 kHz and above the "stop band". We don't really care what happens to the frequencies between the pass band and the stop band: the range from 20 kHz to 22.05 kHz which can't be heard well enough to be worth preserving and doesn't cause aliasing so it doesn't need cutting out. This is difficult because the stop band is only 1.1x the frequency of the pass band -- for you musicians out there, that's less than the difference between C and D on the western scale. (Just think for a minute: design a filter that lets middle C through, but completely filters out the D above.)

Heavens no you wouldn't use a Butterworth filter for such a task. We want an elliptic filter, probably. 3rd order is no good either, it won't give a sharp enough cutoff. 8th order is better. This will get you a cutoff around 20 kHz with something like 60 dB attenuation at 22.05 kHz. People need a lot of these filters, so you can actually go out and buy a 20 kHz low-pass 8th order elliptic filter as a monolithic chip.

Let's suppose you chose a 48 kHz sampling rate instead. Now the stopband starts at 24 kHz instead of 22.05 kHz. It sounds like a small difference (22.05->24 kHz cutoff) but it's actually a factor of 2 (2.05->4 kHz transition band). This means that with the same components, you can get 80 dB or more attenuation in the stop band.

Now go to 96 kHz. You have to design a filter that rolls off between 20 kHz and 48 kHz. That's easy peasy, and you can reduce the ripple, increase the attenuation, maybe reduce the order (affecting noise) and make all sorts of design tradeoffs that are much easier.

Now think about 192 kHz. What's the point? What does 192 kHz get you that 96 kHz doesn't have? It's already easy enough to design a very nice system at 96 kHz. I think 192 kHz is a bunch of bunk as far as audio is concerned.

That's recording. Now let's talk about playback.

Playback is very similar, everything goes in the opposite direction. You start with a digital signal, convert it to analogue, and put it through a low-pass filter. The aliasing noise is still there, except instead of reflecting high frequencies to low ones, it reflects low frequencies to high ones. So you get the same trade-offs.

The difference is that playback requirements are not as difficult as recording requirements. In particular, the required SNR of a playback system is lower than that of a recording system. I think 48 kHz is fine for playback.

The problem is these stupid 192 kHz systems have backers with big names who never bothered to do proper double-blind tests to figure out if the difference is actually perceptible. You can even get a 384 kHz system these days, which would be overengineered for dogs and is more than good enough for bats.