Captain Marvel can't be a member of the Justice League because he has a LOT of shit to deal with in his first years as the champion of magic after so many centuries without one.
So when Superman asks this new hero, who only appears in Fawcett or in world-ending situations, if he wants to join him, he's met with a big, polite "Oh, no thanks."
But Captain Marvel and the League keep bumping into each other.
Zatanna does a spell that the League requested, and Marvel just "POFF" appears and says something like "Guys, I can't let you do this. It's a scale 12 spell, it could cause a rupture in the fabric of this universe. Here, let me redo this for you, sorry, I just need to make sure, okay?"
And someone says "YOU CAN'T DO THAT" and the magic users explain that, yes, yes he can. he is the new champion of magic and he is in fact responsible for keeping magic in its rightful place, making sure it doesn't go ruining the interdimensional worlds or universes, and that this IS his role in magical society and no one in that room can really take away his authority in matters related to magic. They can try, but the chances of success are very low.
So Captain Marvel takes care of it.
Like, are they on a mission to retrieve a magical artifact? Marvel will show up, grab it, and leave because he needs to put it in the rock so it doesn't cause more trouble.
Are they dealing with a cult that's probably going to summon a demon or something? Marvel will probably be there to banish the demon, close the portal, and reprimand Constantine, because why not?
The magical villain that Marvel saw the League having trouble with? Well, just a little finger shock should do the trick to help them take the villain away.
Got a problem with a God? Marvel is there.
Are the portals opening? Captain is in charge.
Have goblins invaded Gotham? Are fairies loose in Metropolis? Are there talking snowmen in Central City? No problem, Captain Marvel is ur guy.
After a while, JL is dying to have him on their team. Or at least let him keep a communicator in case they need to call for help. Because, well, this guy IS super powerful, a HUGE nerd about magical things, and it's MUCH better to have him on their side than not.
But he always refuses, because taking care of all the problems related to magic and Fawcett's stuff is already too much, hes just like 8-9 years old, give him a break.
Yeah but of course one day, after a long day, Superman goes back to Fawcett to ask about it for the thousandth time, and he's so tired of this subject that he just waves his hand and says: "Okay, okay, give me a year to make magical society at least more stable so they can keep going without me present all the time, then I'll go with you, okay?"
And Superman is beaming with happiness, he agrees, leaves, and Billy goes to sleep that night dead of exhaustion on his little couch on the rock of eternity, wondering HOW he's going to make magical society stable after CENTURIES of instability. in. one. year.
That's future billy problem tho, not billy of the present. that being said, time for the champion's nap