Who benefited from the allegation that Richard III killed his nephews? Richard III had the children of Edward IV declared illegitimate by act of Parliament in 1483. Henry VII reversed this act in 1485 so he could marry Elizabeth of York, Edward IV's oldest daughter (Richard III's oldest niece), unifying York and Lancaster. However, this act also legitimized Elizabeth's brothers, if they were still alive. Hence the motivation for alleging Richard III killed his nephews.
There was a revolt in 1487 against Henry VII (Tudor) led by a man claiming to be Richard III's younger nephew. The self-styled Richard IV was recognized by the Duchess of Burgundy, who was Richard III's sister, and the King of Scotland, who married Richard IV to a Scottish noblewoman. This revolt was backed by the Earl of Lincoln, who was Richard III's designated heir, and had no motive to back an imposter over his own claim.
Caxton's printing press gave the Tudors access to one of the world's earliest propaganda machines.
Opinions of Henry VII differ. One of the things his reign is famous for is Morton's Fork, named for Cardinal John Morton, Henry VII's Chancelor and chief tax collector. Cardinal Morton told people he was squeezing one of two things: 1. If you're spending a lot of money, then you must have a lot of money, so you can afford to give some to the king. 2. If you're not spending a lot of money, then you must be saving a lot of money, so you can afford to give some to the king.
Unlike his Yorkist predecessors, Henry VII didn't engage in trade for his own account. He was always broke, so Morten had to raise a lot of money for him.