It is important you identify which deaf you are talking about. Born deaf have very limited access to music and predominantly tend to go for music or output that has strong percussive input, like drums, bass and similar, because of vibrational access, obviously, the voice and many other instruments operate at frequencies they cannot access. Pop music has a greater following than Opera or classical etc for that reason.
With those who have lost all their hearing post-education or rely on limited hearing aid access, then the question is more directed on the psychological point rather than what hearing or not is there to utilise. Trauma plays a leading part in access not only with music but to speech as well. ATR was an amateur musician for years lived music, but on finally losing all hearing saw little or no point in emulating 'Deaf' peers by concentrating on vibratory accessible music, the reasons are complicated.
'Missing what you know is there' is one aspect, knowing which instrument is an essential part of the music etc, the voice of the individual singer and differences that create a following or love of a particular artist etc. Having it signed, or even karaoke can just add to the misery, your ' mind's eye' will recall perhaps aspects of the tune born deaf would never appreciate. All they get is the interpreter's version of things.
On going profound deaf virtually overnight, I decided to get rid of my radio, my instruments, sheet music, and recordings of artists, As you need hearing to follow and I didn't, what was the point? I did attend a deaf accessible gig once and it was a bit farcical to be honest with deaf children running around and others with their heads against the instrument bodies to get an idea what sound they made, but clearly the modus used is vibratory, whether they could distinguish some instruments from another or even pick it out in a concert was debatable. Because an orchestra isn't just one instrument, even with music written especially for it, you will find others involved.
Me trying to follow what I used to be able to when hearing induced depression, so a 'clean break' was the option I took. If I cannot have it all, I don't want to focus on a tiny bit of it and wonder what the rest was about. Very obviously any music that came out after I went deaf is inaccessible. You can try and follow via lyrics but modern music is on par with illiterates and repetitive mostly, and relative, as all music is anyway.
While Beethoven could still write music due to inherent memory (As could I presumably because All Music is basic maths), not hearing it is an issue and 'bouncing off' fellow musicians and being able to ad-lib and be impromptu, is part of the creative process, and that is an issue to deaf people as is importing different instruments and singers etc, the field is quite narrow for born deaf to press on with that.
One thing is a comfort, is in that inherent memory can fill in musical gaps your deafness cannot via mental replay, unfortunately, that restricts you to music you knew pre-deaf. Which meant post 1970 the music died. I have inherent memory of 100s of tunes many I can mentally replay just by reading about it. From Tchaikovsky to John Lennon.
Perhaps I already had the best of it :)