Bob Moog did not invent the idea of a synthesizer. It emerged much earlier in the 20th century, from a mix of electric-powered organs and various other early electronics, with many of the inventors working independently. The boundary between "organ" and "analog synthesizer" has a gray area, and there were some unique pre-Moog instruments like the Theramin. Moog's contribution was to make programmable synthesis more affordable and standardized for professional use - but many of the "synth-like" sounds used in 60's and 70's records are organs with effects pedals put on them; small electronic organs had become affordable in the post-war era.
The distinctive-yet-samey sounds of the 1980's aren't entirely attributable to presets; the presets are a symptom of the underlying appearance of digital technology in music. Digital simultaneously opened up new realms of affordability and privilege - at the same time you got cheap tone boxes like the Casio VL1, you also had monsters like the Synclavier, used on "Thriller" and in many movie soundtracks, with high-end configurations billed in the ballpark of $500,000 dollars(1980's money). Digital gear also changed mixing in favor of extensive production, leading to the heavy reverb washes and gated snares everywhere. Using a "high end" sound was a status symbol, so it was flaunted even if that meant you were using the same orchestra hit as everyone else.
The reappearance of analog is attributable to the same backlash seen in every media market that has experienced a race-to-the-bottom in price points: Synth designers have decided to do an end run around the piracy/DRM/price-pressure issues by going back towards manufacturing. The sounds are "classic" now, and marketed as such, with a few new tricks added to keep up interest. Musicians often get into very idiosyncratic workflows and for some of them, working directly with knobs and patch cables is the right way to go.