I tend to separate "Electronic Music" from synthesiser-based music. One is a very broad church of styles of music while the other is music made using a type of instrument, in my mind they are unrelated.
In 1974 bulk of Tangerine Dreams albums were not synthesiser-based, however, they were electronic and certainly psychedelic avant garde in style. Phaedra marked the beginning of the Berlin School (along with Schulze, Hoenig and Ashra) and the use of synths and sequenced rhythms moved the music away from the avant garde and (in the case of TD) towards a more Progressive Rock style of structured music (such as on Cyclone and Force Majeure). Kraftwerke and Neu! took this several stages further and were a strong influence on the emerging English "electronic" groups of the late 70s of Tubeway Army, Ultravox! and Human League, but that influence was non-existent in bands that followed after them - this is most evident in the style music that those three morphed into during the "New Romantic" era of the 1980s: Synth Pop (there is no real musical connection between Tubeway Army's first album and Numan's pop hits, Foxx-Ultravox!'s System of Romance and Ure-Ultravox's Vienna or The League's chart-flopping Reproduction and the chart-topping Dare).
Once the Pop world discovered the synthesiser and started making Synth Pop any connection with "traditional" electronic music was broken, even Depeche Mode with their seemingly Köln-inspired industrial Synth-Pop were simply following after Ultravox, Bowie/Eno/Berlin and OMD - the influence of Conny Plank was secondhand. All subsequent popular synth-based music (ie Dance Music) is a derivation from those early 80s Synth-Pop origins, not from traditional electronic music or electro-acoustic music or even some of the more rock-oriented electronic music (T.O.N.T.O, Synergy, Jarre, Vangelis et al) or classical-inspired synth music (Carlos, Tomita, Kitarō). It is only in recent times we've attempted to join the dots and relate one back to the other, so with modern IDM music we see a connection that perhaps does not exist because we want the "I" to mean more, (just as some what to see the "Progressive" in Prog Rock to be adjectival and not just as a meaningless noun), for Intelligent Dance Music not to be a derogatory oxymoron in our personal music appreciation libraries we need to make that connection back to more loftier music, whereas perhaps what we really mean is simply "Interesting" Dance Music. (all hail the Aphex Twin). The generation gap is a physical gap with few crossing places.
Even with "ambient" electronic the direct line-of-sight connections between the minimalistic, avant garde of the Reich and Riley to Eno to The Orb to FSOL to Coil to Tribes of Neurot to Amber Asylum to Burzum to Mortiis to Merzbow to Bass Communion is perhaps more of an illusion than at first meets the eye (or ear).
The primary role of the synthesiser in a Rock band was no different to the Mellotron, it was there to provide orchestral backing, not as a lead instrument or as the sole instrument. Prior to the creation of the synth (and that means the analogue and/or digital synthesis of tone) this musical polyfiller required employing a small studio orchestra, heard at its worse on productions such as Genesis To Relevation and David Bowie's first eponymous album. Even in most Prog Rock bands the synth was there to bulk-out the production, (not every band had an Emerson or a Wakeman), just as the Moody Blues and King Crimson used the Mellotron, or it was used as a gimmicky sound effect (cue Roxy Music), or disparagingly rejected (Queen) - it some respects it took Pink Floyd to open Pandora's box of delights and show what the synth could do as the primary instrument in a piece of music (and even "On The Run" was met with a wave of criticism back in '73 for being "computer generated").
The Sampling Synth was a different beast - now the keyboardist could not only play every instrument in the orchestra, he could create new sounds and replace the whole band - music created using the sampling synth can produce music in any style, be that rock, classical, ambient, jazz , this does not make all music created using it "electronic music". Nor do I believe that guitar-based music is niche or marginalised anymore now than it has ever been - we would not have described Motown or soul music as either guitar or synthesiser based music yet the modern Pop world still seems to be dominated by R&B artists such as Beyoncé, Adele, Rhianna regardless of what instruments are used to provide the backing music to their plaintive caterwauling.