Imo, the Yonkou system can disappear after the discovery of the One Piece, however piracy will continue to exist. I mean, not every pirate is after the One Piece. Some wants power, some wants to plunder, etc...
So there will be powerful pirates who stand out from the rest.
First, we have pirates who own countries : Boa Hancock and we can put Katakuri in this category given he's now the head of the Big Mom pirates who own Whole Cake Island.
If Doffy and his family happen to get out of jail, Doffy might also be part of those powerful pitates.
And I saw above Yamato. Yamato has actually a shot to become a powerful pirate.
And I think that's it.
Because Law will have no reasons anymore to sail once he will discover the meaning of D.
Kid will have no reasons anymore to sail once the One Piece will be found.
And the renmants of the Whitebeard pirates will stay disbanded forever imo (except maybe for the final war).