For me there are two aspects. First is directly related to your question, which is that vinyl has stricter limitations on the mastering[1] compared to digital. Some might prefer the sound that results from these limitations, at least when well done.
But for me it's mostly about the ceremony around playing a record. You have to actively participate, preparing the player, and you sit down and listen to the record in linear order. No fast skipping. So when I listen to vinyl it's about relaxing and enjoying the music for what it is.
I'll bet dollars that this is the unqualifiable difference between vinyl-analog v. digital; if there are specific mastering constraints, it sounds like e.g. the timbre of certain sounds/instruments would be affected, likely to the benefit of our ears since the sounds most impacted tend to give the harshness that some people complain about with digital presentation.
> The vinyl medium does not “like” a lot of high frequency information — brightness/hotness of certain high frequencies are the most common issue we see on the audio masters we receive. Instruments such as hi-hats, cymbals and tambourines often cause distortion if all high end is allowed to pass through to the cutting lathe. Vocals that contain a lot of “SSSS” sounds (sibilance) will also cause a distorted sound on your master recording if not properly treated.
But for me it's mostly about the ceremony around playing a record. You have to actively participate, preparing the player, and you sit down and listen to the record in linear order. No fast skipping. So when I listen to vinyl it's about relaxing and enjoying the music for what it is.
[1]: https://www.gottagrooverecords.com/vinyl-mastering/