Fantastic OP! Really covers whats memorable about this game.
I honestly feel GTA V surpasses San Andreas in almost every way. As you pointed out the soundtrack to San Andreas is a masterpiece, and is one area where I feel GTA V came up short. Outside of that, GTA V is a superior game in every other regard.
In all honesty this sounds like nostalgia. The missions in GTA V are way better designed than the missions in San Andreas. I don't remember coming across nearly as many terribly designed missions in GTA V as I did in San Andreas. The chasing the train on the motorcycle one still sticks out in my head as a terrible mission. The core gameplay is VASTLY SUPERIOR in GTA V. Everything from movement to weapon handling is just on a completley different level than San Andreas. The terrible aiming mechanic almost makes San Andreas unplayable in comparison to GTA V.
I really like San Andreas, and even thought it did things better than GTA IV, but at this point I think it's time to realize that it has been comprehensively surpassed.
Thanks for reading. You know, if you look into things objectively, all 3D era GTA's have aged pretty awkwardly. Controls wasn't something special even for back then, but every flaw in the mechanics was covered because we still were in the "tank control" era anyway. The structure of some missions was pretty bad designed as you say, but there's a thing i miss from the 3D-era games which is the absolute freedom given in any mission on how you complete each objective. Things have gotten more linear after GTA IV when you had to do things in a certain way.
But overall, the HD era games are on a completely different level. When i first booted GTA IV i was completely shocked by the detail on every aspect of the game. In retrospective, goin back in 3D era games looks like everything is made on low-res, low-poly paper-like textures (which is true). Then GTA V came and everyone gone bananas, but that's another story.
Going back, there's still plenty of fun in the core 3D era games nevertheless.