Shuffling teams between conference is whole other thing. Probably a bit more difficult to do too. It would mean less rivalry (and calculating rivals every seasons). If totally random, it wouldn't solve the risk of having uneven quality between conferences. Even if not random, uneven conference could still happen depending on early season choices by managers. And usually, it does sort it out itself after some seasons.
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Mixing the conferences is really necessary.
Look at ACBB (Spain div I)
It is several seasons that left/blue conference is definitely stronger than red one.
And same happen in main of leagues and divisions
I suggest that the positions 2,4,6 of every conf change the next season and system trĂes to collocate promoted and demoted teams trying to compensate the level of the conferences.
There is no guarantee finally the conferences will be even, but it is a way to try to get it
S52 CUP WINNER "non dire gatto se non ce l'hai nel sacco"