How does sound influence your appreciation?

It depends on the system, to me. Many systems are oriented towards scraping and exposing the most minute details. These will present the venue and mastering and can mask the music... drawing emphasis to the system. I used to have one of these. To me this restricted my appreciation to the very finest recordings and as close to my core preferences in music.

Alternatively very musical natural systems present the venue and mastering in proportion to how they would be in real life, if you were there. In this case, the system I have now, will draw me in to all sorts of music that I would never like normally. Another major parameters that draws me in is the rhythm and pace... here music with a very good beat will really suck me in... I’m thinking of pop and some other genre I normally do not like.

I think it’s true that better sound quality helps with getting into unfamiliar music and genres as has been said already.

Arguably, that’s more important than giving fresh perspectives on old favourites. Is it really that big a deal to hear parts of the mix that previously went unnoticed?

Definitely the case for me. I have developed a huge appreciation for jazz as my system has improved. Listening to it in my car is not nearly as engaging or rewarding. 

Over the years I've found myself looking for well recorded music.... clarity maybe even first over content but I do have to like the music first.

If I don’t like an interpretation, great sound isn’t going to help.  A pig doesn’t look any more appealing when being viewed with binoculars