yates7592, a good P.A. system might have a 12 kHz bandwidth. During a live performance there will almost certainly be some sound energy above that limit as the result of non-linear distortion. (Spurious sound energy is also produced at frequencies in the main part of the audible band, of course; it doesn't just "go up" in frequency.) Whether that distortion is beneficial or harmful is entirely a matter of personal opinion. It's part of the live sonic experience, and I could agree with anyone who feels that it should be captured in a recording. Also, I don't know what anyone could do about it if they considered it to be harmful; you can't "record around it."
The same issue came up in the 1980s when CDs were introduced to the public. Defenders of vinyl showed that the playback of vinyl LPs often includes sonic information above 20 kHz which the CD couldn't reproduce. However, when you consider the limits of studio microphones, tape recorders, disc lathes and the whole vinyl pressing and playback process, you realize that very little of that "information" was put there by the record company! Rather, it was mostly tracing distortion--a fact which the vinyl advocates didn't generally choose to mention.
Most home loudspeakers are doing well if they can reproduce 18-20 kHz cleanly. If you record signals beyond 20 kHz, playing them back through an amplifier and loudspeakers can cause audible artifacts. Again this may be experienced as subjectively pleasant, unpleasant or neutral--but since this can also happen with signals that are below the Nyquist limit for 44.1 kHz sampling, as far as this is concerned it might not even make much difference what sampling rate is chosen for the recording.
Some 96 kHz converters are technically and, potentially at least, audibly superior to some 44.1 kHz converters, while some 44.1 kHz converters are technically and, potentially at least, audibly superior to some other 96 kHz converters. There's no such thing as 44.1 kHz sampling having one certain level of quality and 96 kHz sampling having a certain other level of quality. There are only specific implementations that use those two sample rates. In many cases the bandpass filtering rather than the conversion (as such) has the greater effect on sound quality.
--best regards