Samy Duc wrote a really good deep dive into Apex Legends matchmaking that covers skill and team balancing: https://www.ea.com/games/apex-legends/news/matchmaking-2023
In terms of overall experience, the best approach in general is a purely random one. This is how you avoid the experience of getting trapped in a 20 game losing streak, even if you are a really good player.
If you allow the natural balance of good players winning more often and bad players losing more often, you will find things get a lot less messy in between. This also provides your bad players an opportunity to occasionally witness what they could become. When you only play someone 1% stronger than yourself, you probably don't have a great idea of what the upper bound actually feels like. This can become a serious trap for players who are seeking to grow their skills.
While I also have fond memories of pre-SBMM Halo/CoD from the 2000s, they're more focused on pure shooter mechanics rather forcing players to work together to win an objective, so doing well but losing still feels fine. I find SBMM is needed in more objective focused esport games like overwatch, because the game is designed such that it's harder to do well individually (and thus have any fun) if your teammates aren't doing well.
Perhaps this is the actual cursed aspect. In a free-for-all context (i.e. a team size of one), you would never have this kind of a problem. As you increase the mandatory team size to six, you are creating an entirely new universe of effects to compensate for.
In my experience, 99.99%+ of the frustration in Overwatch and League of Legends emerges from dealing with your own teammates, not your opponents.
For a few of the games I worked on, random matchmaking like you describe is a non-starter. If you're a 90th percentile player in one of our games, you effectively never lose to a 70th percentile player or below. Your rating will be so high that we can't give you any rating system points for the win. So the person who won got no reward other than the feeling of winning, and the person who lost played a match they had no hope of winning. It ends up feeling pointless to play as a top player because only 1 or 2 matches in 10 on average have any meaning for you. Needless to say, it also feels worse as a low rated player because you simply lose more often.