I think it goes back a long way into the 70's with greats such as Edgar Froese from Tangerine Dream (RIP) and people like Klaus Schulze, Jarre, Kraftwerk, and many others. The Moog modular was up and running in the mid 60's so it was well established by the early 70's. Tape saturation and how tape interacts with analog synthesisers was definitely a situation that was around then. It was the only situation at the time some very great albums were recorded.
Reel to reel machines don't record and playback square waves very well and they tend to generate lots of distortion that adds tone and colour and harmonics to our input signals and that can be analog synths too.
I am fortunate to have owned and used some high quality analog synths such as Moog, Oberheim, Sequential, Roland, Korg modular etc.. and how they sound when recorded into multitrack analog tape medium was an important consideration. The tape changed the sound of the synth further again. I had first hand experience with it. You could either use it or compensate for it. I often did both.
I still have some great sounding hardware now and believe me digital records and plays them back better now and more accurately than ever before. But what do you do when you generating the sound from a VST and it may have quite a dry digital sound to it.
(especially when it is pretending to sound like an analog synth too!) Then yes I say use all the plug-ins now which are available and sound rather excellent too without the hassle of the multitrack/stereo machine.
These days we have it good. We can also send
part of our mix too to the saturation farm and back for some semi saturated effects within a total mix. I agree with
sharke too about how great and amazing some very clean and dry sounds can be as well. I love it. It seems that to me the synths that are winning in these areas are the finest virtual devices we have now too. And sometimes these things are just best left alone and hear them the way they are meant to sound. For me I love the balance of great sounding hardware combined with the fine virtual instruments.
The genre arguments are a bit boring I think. Everything has been done a long time before by great people such as Edgar Froese. You hear elements of all modern dance tracks in his music. He was setting up the same ideas using similar sounds decades before. People like Edgar Froese just kept on going right up until the end still refining his own personal sounds and ideas and musical concepts. But the EDM guys have zoomed in onto smaller parts of many a great electronic music pioneer's ideas or sounds perhaps and seriously developed and turned it into a whole new culture all by itself.
I always felt the drum machine and sounds were weak/wimpy even back in the 70's for example but now we have the thundering grooves to go with the electronic ideas many of which are born out of ideas well before. I really like the way things develop musically.
A lot of EDM dance music is boring especially harmonically and it is actually not saying much at all. It could be better. But it has been developed for a different need and part of the music industry. I would love to hear more complex harmony in the music perhaps combined with the power of the dance feel of EDM. And throw in world rhythms too just for fun. It would then kick arse!