A lot of the argument has to do with hearing. Younger people and those who have very fine tuned hearing, like violinists, can grasp the extended range of *analog* music, which is above and below what most people can hear, but is also “in between” what most people can hear.
This makes sense if you imagine digital music as being like a staircase, in which every step is a note, but there are no “half-steps” between notes. So there is no slightly sharp or slightly flat, and non-notes, like the squeak of fingers on strings, which are edited out. Digital means yes or no, not maybe.
As far as clicks and pops on analog, that is a mechanical problem. If someone was to create a record player that used an “analog laser” instead of a needle, this wouldn’t be a problem. Digital laser needles have been around since 1977, but that still has the digital problem.
A clear advantage of digital is that it captures a lot more data to start with. So very soft sounds become far more obvious.
There are laser turntables for vynal. My hearing has gone too much for me to bother with it all. I buy CDs then rip them to the highest quality I can.
I have noticed though, that older CDs like Dark Side of the Moon, which is the first CD I ever bought, really need to be brought into a sound editing program to adjust levels though. Same with all my ols Police CDs. They sound like crap unless I pre-process them a little in Audacity first before converting to mp3.