No.
Then WoW would be far more generic fantasy and far less interesting.
The Night Elves would have become generic Dark Elves with a side of Wood Elf, and we'd be raiding their raids, and plundering their dungeons. The Nightborne would likely have been bad guys too, and we'd basically have seen those two groups and the Naga (and the Satyrs) as the same generic "mostly evil" elves. Teldrassil would have been a raid or two like AQ (I know someone is desperately jacking off to this idea but it wouldn't have been much fun).
The Forsaken would be completely generic undead being slaughtered by the boatload, and would never have become developed as individuals with thoughts and so on (which wasn't really much of a "thing" in WC3 - it's not until WoW that it happened, and it wouldn't have happened if they weren't playable). Sylvanas would have been a raid boss, probably in Vanilla, likely associated with Naxx (or instead of Naxx).
The Horde would have thus been a one-note collection of "Barbarian-type races". The Alliance would have been a one-note collection of "Civilized races". I mean, fuck me, you're condemning us to a future where the core Alliance races were Human, Dwarves and GNOMES for god's sake. The counter-notes of the Forsaken and Night Elves not being present would have made things vastly more boring and simplistic. It would also have meant that it was harder to add races which didn't fit the existing theme to each side.
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Fuck me, you don't even actually play WoW, do you? THEY HAVE FUCKING SHARP FANGS. That was one of the first things I noticed when I played WoW in 2004 (on males where they're more prominent, admittedly, someone with Classic beta can hope get a screenshot showing whether females do - pretty sure they do).
https://www.mmo-champion.com/content...-Model?page=17
Fuck's sake, right here on MMO Champion "Fangs confirmed".
More evidence that you've never played WoW. You seem to be confusing it with TERA or some shit.