Except it wouldn’t.
For one thing, the increase in the number of players means increased que times; with random team races, that’s not really too much of an issue, though it does present some issues with matchmaking specifically around the variability of MMR. However, this increases tenfold when you then force mirrored teams as you’re suggesting, making MMR disparity far greater than we have already (and for some team games, it can be pretty rough if you’re playing random teams), and making queue times intolerably long.
And that’s without considering the other myriad of issues that your stupid suggestion would come with.
More importantly, the game isn’t balanced around team-games, but balanced around 1v1. As a direct result, you’re always going to have overpowered combinations regardless of whether they’re random or mirrored teams.
Forcing mirrored teams would actively inhibit what you’re trying to do too, because you’re always going to be facing the same team that you’re playing, inevitably leading to stale matchups.
1v1 has the advantage of having the player play against 3 different races, regardless of what race they’re playing themselves. This directly opens up variety of play from that alone, because it changes the matchup constantly.
With forced mirror teams, you actively restrict the matchups to ONE matchup, regardless of any combination that you’re running. If you’re playing T/P, then your opponent will always be T/P. if you’re playing T/Z, then your opponent will always be T/Z. If you’re playing Z/P, then your opponent will always be Z/P. As a direct result, there will never be any variation in your openers. There will never be any variation in what and how you play.
Your suggestion is, as always, terrible, and you should feel terrible for even allowing such a genuinely stupid thought to pass through your mind, let alone giving it actual consideration.