Alan Parsons Project only had two official members (Alan Parsons and Eric Wolfson) and lots of session men and guests, even though many of them appeared on most albums. Parsons was not known as a musician and Wolfson was pretty much anonymous when the band was formed.
Trio of Doom John McLaughlin Jaco Pastorius Tony Williams Short-lived and better on paper than in reality, but potentially extra super.
The answer is so clearly The Traveling Wilbury’s but I’m surprised no one has mentioned the Foo Fighters. A band consisting of one part Nirvana, one part The Germs, and two parts Sunny Day Real Estate. They have inarguably had the largest career of any super group I can think of.
I suppose it was just for two shows, but the band Steve Hackett but together for his Tokyo concerts was a real supergroup: Hackett- Genesis, solo and GTR John Wetton - King Crimson, UK, Asia Ian McDonald - King Crimson, Foreigner Chester Thompson - Zappa, Weather Report, Genesis Julian Colbeck - John Miles , Anderson Bruford, Wakeman and Howe, plus Hackett's band. And they delivered great shows.
Probably because when the Foo Fighters started, it was just Dave Grohl. (For 99.5 % of the first album. Greg Duli from the Afghan Wigs played a couple of guitar parts.) The rest were brought in as backing musicians when he needed to tour. By the second album, then they became a “real” band, but again, that lineup only lasted for one album.
There has been a lot of lineup changes but 3 out of the 4 are still in the lineup today and all 4 on their biggest album. I don’t think they viewed themselves as a super group but looking back the band consisted of major members of three seminal bands.
I like the list in the original post. It would make a good start for evaluating on member talent. The Traveling Wilburys must be one of the strongest bands ever, supergroup or otherwise, in songwriting ability, even with some of the members long past their writing prime. However, even the best songs on Volume 1 don't approach the lyrical greatness on members' own albums. And Volume 3 is a dud. Yet another supergroup that didn't try very hard to do its best and existed mainly to have fun. Bad English had 2 very good songwriters with a knack for writing hits (in a genre and era people here don't seem to like). The band also had a very high level of musicianship (including a quality vocalist, unlike many supergroups). And it was an official 5-band unit, which is very large by supergroup standards and gave it extra firepower. I don't know which supergroup had the most talent on the instruments. There are some 'supergroups' in this thread that I've never heard of.