William has 3 Direct Heirs now... (to say nothing of still having Charles ahead of him when Elizabeth eventually passes)
Barring a 'King Ralph' scenario Harry was never going to see the throne... so why should it be so hard to cleave him from the family tree?
if it were all about 'not being Chuck's Kid', surely they would have cut him off back when he as still going full 'Roger Clinton'/'Billy Carter'