I don't see Richard as being as obviously the immediate beneficiary as you do, Roxana---he'd already "de-legitimated" them, and the concurrent de-legitimization of his nieces would be a non-issue, since his own claim didn't rely partly on his marriage.

Henry, on the other hand, looks like a very different matter, to me, needing his brothers-in-laws' claims to be off the table, but wanting his wife's claim to be very much "live", for those for whom "to the victor goes the spoils" didn't suffice. With Elizabeth's (legitimate) claim joined to his, the claims of his nephew Edward, and his sister's son John are non-starters.

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It is hard to convey five-dimensional ideas in a language evolved to scream defiance at the monkeys in the next tree. -- The Science of Discworld III: Darwin's Watch, by Terry Pratchett, Ian Stewart & Jack Cohen