I think Battle.net was a force multiplier. C&C/Westwood had nothing like that. Before the internet became a big thing, I think C&C actually had the edge over Warcraft 2. It was very popular at the time. They just sort of fell off with the sequels in popularity, Starcraft hit at the exact right time that every serious gamer was starting to get decent internet access and was familiarized with it, throw in Battle.net being at the time a huge outlier in terms of ease of use (anyone who remembers all those random online game services back then like Gamestorm knows what I'm talking about, other game franchises outside of Blizzard were often just a huge fucking annoyance to get MP setup).
Starcraft was definitely a good game for the time, but it's incredibly unfortunate that it made all devs after that point focus on micro-heavy RTS design, that killed the old appeal of basebuilding RTS and I think prematurely buried the genre. There was a large contingent of old school/more casual RTS gamers who were left orphaned and with no games to play, and eventually that withered away into no interest for the genre overall.