"Why do you think there should be a team game rating?"
Because that team games and 1v1 games requires different skills to some degree.
Optimal play in team games require coordination, team work and communication between players while 1v1 requires none of that. Some skills that are more important in 1v1 is raiding, expanding and trading your units off for momentum and map control, while unit preservation, ecoing, reclaiming and knowing lategame units is more important in team games.
"When it comes to accurately rating players, there's no point having more than a single, combined rating. Even including games on trollmaps improves the rating accuracy."
I don't see how troll maps could increase rating accuracy. If you take maps like Duke Nukem where you can easily lose because of RNG, how will that make rating more accurate? Imagine a map where the only that thing decides the victor is a literal throw of the dice, how can that make rating more accurate?
If you take maps like Speed Metal, Cow or other strange maps, they might still require skill to win but this skillset is different from 1v1.
Now, 1v1 is surely the fastest way to get accurate information about the general skill of the individual player.
After all, if it is a 10vs10 team game, on average, individual players only have about 10% impact on the outcome of the game. It takes many more games to average the skill of the player in those situations.
However, if I have played many teamgames and suddenly jumps far above everyone else just from playing a few 1v1. Then something is wrong.