Henry IV has living descendants, not many, but 3 gateways, tnrough an illegitimate granddaughter.
Edward IV has descendants through 2 bastards, but no gateways.
Richard II, Henry V, Henry VI, Edward V, and Richard III have no descendants.
The next king with legitimate descendants was Henry VII, 150 years after Edward III, but his descendants were a much smaller and more exclusive class than Edward III's.
This list is very interesting
https://familypedia.wikia.org/wiki/Descent_of_Elizabeth_II_from_William_I
From William down to Edward III, every generation wore the crown, if you include Matilda. From George I to the Queen, only 2 generations are skipped. But between Edward III and George I, of 13 generations, only 2 wore the crown.
The rest of the time, the throne was occupied by branches which had the better claim, one way or another, but then fizzled out, one way or another.
This is fairly typical of how titles descend. If you trace the direct line back from the current peer or baronet back to tne 1st, there can be a lot of generations that didn't have the title. And if they brag about their illustrious "ancestors", often those "ancestors" weren't in their line.
Philippa of Clarence, #11 in tne list, has many gateways, but she died as heiress presumptive. If she'd lived longer, the descendants of Queen Philippa would have had bragging rights over the only-Edward-III bunch.
