A lot of the time they don't mean analogue when they say they don't want digital - they mean that they want knobs and switches to play with. I think some modern Moog's even have a digital stage in the signal path (I might be making that up but I have some vague recollection of it in a schematic)

Making a synth sound good has very little to do whether it uses analogue or digital synthesis these days, but analogue equipment is (for the same price) less reliable, uses more power, less flexible, and more susceptible to being damaged by impacts (and keep in mind that you can't repair a lot of modern gear with SMD soldering experience anyway)

I gigged around Boston in the early 2000's playing guitar in various rock and metal bands, usually in front of 15-20 people. I had been using a 1960's Fender Bassman and changed out the tubes to some Sovtek ones. Sound guy at one of the clubs (who's had been around for 20+ years at that point and seen everything) noticed right away and asked why my amp sounded off. A little while later I bought one of the first Line 6 modeling amps and my first gig with it the same sound guy said "Ahh, you put the old tubes back in". I'm like, "Nope, totally different amp, and it's all digital.". He didn't believe me and while he was inspecting the amp kept saying "No, no, no. There's tubes in here I can smell them warming up".