Recently I came across this profile and I have realized that there is a small category of elite users that are active on several Stack Exchange sites.
Why is there no user combined-flair league similar to this one?
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Because reputation isn't inter-exchangeable among sites. 1000 reputation on Seasoned Advice means a lot more than on Stack Overflow. This is just because it is harder to gain reputation on smaller sites since often the number of voters are lower. Even on a single site it is hard to measure reputation, since very active tags tend to attract more voters than smaller tags.
That would mean that the overall reputation chart will be dominated by Stack Overflow users, just because it is easier to gain reputation there, which wouldn't be fair.
As described by @PatrickHofman, Stack Overflow has the highest frequency in terms of votes and question asked as compared to other sites, which in turn generates a high amount of reputation for long-standing and active user. Most of the users on SO have been inactive for a long period of time, yet still they are getting reputation from one of their oldest most viewed Q&A. Which makes concrete the fact that they will dominate the combined league and due to this the combined league is less susceptible to change.
You can use the query below to see there are many SO users in combined rep rank.