In progressive rock (and psychedelic etc) the use of bleeding edge technology to create new sounds has always been a thing. In that genre the transition from organs to synths was really a rather trivial transition for the most part, it was just basically getting the latest models of the things they'd been using anyway. This is also quite apparent from the way they used synths. It was more a big deal for the fans than it was ever musically.
The way prog bands used synths/organs however has relatively little to do where synthpop came from. Even though it's not obvious at the other end, synthpop is part of a rather direct musical heritage that goes
punk -> post-punk -> new wave -> synthpop. (Synthpop is sometimes categorized as a subgenre of New Wave. IMO this is highly inaccurate, but let's not fight about that
)
Obviously this is a huge simplifcation of the history of those genres, but when you remember that whole transition happened in less than a decade (late seventies to mid eighties), it's pretty easy to understand how some things were the way they were in synthpop. It might not be obvious that synthpop was grandfathered by punk, but the aesthetic preference of keeping it simple was still very much there.
Of course classic disco music was another influence.