While Elo (and side note: it's a person's name, not an acronym) isn't perfect and systems like Glicko-2 are better even for 1v1s, is there a better system than Elo that could be used to rate players in team games? Especially if there's a mix of pre-made teams and random teams thrown together by matchmaking?
Edit: extra bonus if it can be applicable in games that have both 1v1 and team game components where there might be a desire for some form of bleed between the two. (e.g. AoE2 where your starting Elo in one of them is based on your Elo in the other, if you've played a lot of one type of game before trying the other.)
That sounds kinda similar to how AoE4 does it, albeit with fewer of the more complex guard rails.
The game only displays your "rating", which resets each season and is used to place you into a certain league. You have two ratings: 1v1 and Team Game. There's slight upward pressure so if you keep playing you should on average climb. At the end of the season you get some basic cosmetic rewards (profile pictures etc.) based on the highest Ranking achieved throughout the season.
The game also keeps a hidden MMR/Elo. That does not reset each season and is the tool actually used by the matchmaking system to decide who you will be playing against. It's a true Elo system, or possibly an Elo-like system such as Glicko. The game keeps track of separate MMR for 1v1, 2v2, 3v3, and 4v4.