You don't need a new reason to create cadet branches. You already have the same reason Lowborns are assigned a random dynastic name when they become lords: an enormous monolithic dynasty is completely broken. You definitely don't want to give the player (or AI) incentive to split off cadet branches as this would mean they'd get even more advantages than they already getting for spread their dynasty over the map.
As WingedLion14 says, the best way would be to have it work as it did historically: if a junior branch of the dynasty holds a title, they become "of Title", "Title" or they form a name based on the given name of the cadet who received the title. Possibly they could hyphenate in the old dynasty name or retain some ties with the main branch, but the more important thing, from a gameplay perspective, is breaking up the mammoth dynasties.
As WingedLion14 says, the best way would be to have it work as it did historically: if a junior branch of the dynasty holds a title, they become "of Title", "Title" or they form a name based on the given name of the cadet who received the title. Possibly they could hyphenate in the old dynasty name or retain some ties with the main branch, but the more important thing, from a gameplay perspective, is breaking up the mammoth dynasties.