my question wasn't making a point, it was an actual question that I was hoping an answer for to determine how the situation should be approached.
You're raising issues that don't really exist.
The hypothetical situations you raise are pointless. In your situation, assuming we use the type of algorithm you propose to determine the skill of teams, there are now 20 teams that Jaice is a part of on the list of teams (just because of one person, let alone the 50 others who may switch between partners; lots of clutter). But there's also no way to determine which time is better, other than a theoretical algorithm. It may say that one team is better than another, but only in theory; the teams would need to face each other to determine that, which can't happen. Then this process would have to happen with every person.
If what you said, were to happen, the list of best teams would be:
1. Jaice + 2nd best
2. Jaice + 3rd best
3. Jaice + 4th best
4. Jaice + 5th best
and so on.
It not only would just look ridiculous to have one person in every (or even multiple) team(s) as 'the best teams' but also impossible to determine which is the best amongst those as they cannot battle eachother.
No data will ever be 100% accurate, players and results are constantly changing, and at any given time someone's elo may not represent their skill.
With set teams, there are constant variables that are pit against each other over a period of time.
Within this set of teams, a ranking order would be able to be established (and one person won't be in multiple teams that will be unable to face each other).
From this, a more accurate PR can be established.
Using that algorithm and making a new team and scoring them based on who is teaming, that will only result in the top 10 being 5 teams with jaice and 5 teams with jezmo.
With mine, yes unfortunately only set teams would be able to be eligible for ranking/PR in one season; which would exclude unofficial teams that may or may not place better than official teams.
However, I'd rather a few one-off teams slip through the cracks than have an entire list of teams be made up of one person holding the top several ranks with [insert random players]. Again, even with that list which would look ridiculous, there's no way of determining which is better among them.
It would also encourage those who do want official doubles rankings, to have an official team; while those who do not care or not want one, continue to have different doubles partners each time.
It's just not viable to have a system that tries to rank every combination of players, as that way the teams that play against each other will be different each time and impossible to accurately show improve because of the number of variables (hence why we don't already have it), let alone one person can't be on two teams at once to determine which of the two (or more) they are a part of is better.
You can do it all hypothetically with the algorithm as said but that's not reflective of actual doubles results between the various teams.
I just don't see your way as a viable or accurate way to determine the best teams.