Firstly, the “Yonko System” isn’t an actual system so much as the New World’s equalibrium. The World Government doesn’t have a powerful enough presence in the New World to provide the islands and kingdoms with any sort of protection against pirates, so how do they stay safe? By being subordinate to the biggest, baddest pirates in the sea.
Lesser crews like Brownbeard, Don Kreig, etc.. could surely harass a number of islands in the New World but would likely avoid it if they risked angering an incredibly powerful pirate crew in doing so, by this logic Islands look to the strongest pirates for protection and congregate under a select few, most powerful pirates, thus forming the basis for Yonko Terriories.
Now, why can’t Kid or Law become Emperors?
Despite the fact they ‘beat’ Big Mom, they lack the power to do so individually. So if one claims the title and Big Mom persues the one who does or goes after a territory that defects to them (since she’s known to hold grudges) Kid or Law would be helpless against the full might of the Big Mom Pirates.
Which leads me to the next point, neither crew is capable of maintaining territories. They both have less than 30 crew members so they couldn’t possibly defend Big Mom’s territory if they took it. This is how Blackbeard was able to usurp whitebeard, he had power, able to defeat the Whitebeard Pirates head on, AND able to claim his territories.
This is also why Luffy would be able to replace Kaido as a Yonko if he wins. He’ll have beaten the Beasts Pirates crew in its entirety, beat Kaido in (essentially) 1v1 combat in his own territory, AND has the Grand Fleet to act as enforcers to maintain security over Wano (assuming the samurai don’t join as part of Luffy’s Fleet) as well as the rest of Kaido’s territory.