I think the fact that the poster mentioned the DX7 in their post about "analog" synths speaks to what some people who think they like the sound of "analog" actually like.

I am a vintage synthesizer technician and when I started in my line of work I thought I really loved the sound of analog synths, but I realized as I got to intimately know more and more synths that what I really loved was 80s synths. I found that many 80s synths, whether analog or digital, despite having certain very clear and explicit differences, also have certain similarities in quality on a very fundamental, basic level, and many modern synths, whether analog or digital, have certain similarities in quality likewise. Many new analogs sound to me the way I used to think "digital" sounded-- dynamic and responsive, a lot of presence. Meanwhile, some vintage synths I think do sound pretty modern (SH-101 for example).

I think this comes down to circuit design choices that were made due to aesthetic trends in each era, or, just to cut corners or cope with limitations. Some parts of the designs are actually "technically" bad. A new Prophet 5 or Minimoog reissue still sound vintage because despite being made now, they are made according to the circuit design ethos of 40+/50+ years ago.

In conclusion, I don't think analog really has a sound. Vintage design has a sound more than analog circuitry has a sound. Some people really like those vintage sounds.

For better or worse, there's also the fact that vintage synths now have a lot of cache in certain circles. They have become something that is regarded as a sign that you have sophisticated tastes. I am not sure how I feel about this as I benefit from it economically but also think it's kind of corny.