Yes, I have my doubts about Warbeck too. But Henry 7 certainly had other doubts - and after viciously and horribly torturing and murdering him - he destroyed his face. Very uncommon to do that but people thought that handsome Warbeck facially resembled the young prince.
Actually, as I remember, after his confession he kept him in the Court unharmed for quite sometime. It was only after Warbeck left and mounted another attempt at gathering followers did the King resort to execution.
I think that the King thinking that this character might turn out to be some bastard descendent, didn’t want him abused as a commoner criminal, he wanted to protect himself from critics. Only after those supporting Warbeck against the king made another go at it was the King forced to finally take him permanently out of play.
The era of the Plantagenet’s and the Tudors is of epic sweep. The characters and events are beyond anything a novelist could write.