I think it can be argued that, in small scale skirmishes (as depicted during gameplay), the power levels are comparable or at the very least, I don't have any problem buying it as such. On the other hand, at a larger scale, technically speaking, this is easily Protoss>Terran>Zerg. I've touched on this before but, at this scale, you start talking about WMDs and both the Protoss and Terrans have some really OP crap. When you can destroy planets and such, the zergs have very little chance. Even their greatest advantage, reproducing quickly and swarming, isn't much of a threat when both the Terrans and Protoss have the ability to make robots. I guess they could give Covid-19 to everyone

(why is there no real bio weapons btw? hello?! no "real" zerg virus? really?!)
That's one of the big problem I have with the Starcraft story. There's a lot of "well I know you can do X so why don't you do it?" and you have to use a lot of head canon to answer those. It's written like Harry Potter really. Characters(or factions) can do anything but the author doesn't explore what any of it really means as part of the universe. Instead, the author push the narrative that he wants without bothering with the larger implications of the things he previously introduced. It's not necessarily bad, I like Harry Potter lol, but you do offer a different experience when you write this way. A less serious one and I'll admit that I do a lot of eye rolling when they then try to do a 360 and make it look serious. Like, if they kill off a character and try to make a long dramatic moment, there's less emotional impact because you're just like "well you could have just done xyz and we wouldn't be there, this is dumb". Dramatic moments like that aren't really a SC1 story thing though(thankfully), but Blizzard does that stuff A LOT otherwise (looking at WoW >.>).
Anyways, I think it would have been cool actually if the story fully explored macro strategies that the 3 races would have naturally employed. It would not affect the gameplay because there are still reasons to fight at a smaller scale so that wouldn't be a problem. In fact, it could have given a pretty nice flair to the mission design.