"Asserting that Robert de Welles is not the son of Sir John Welles, KG, 1st Viscount Welles does not move the issue forward."
It is pretty much the entire issue.
"There is no doubt that Sir John is not his birth father. What is not in dispute is that Robert de Welles is the son of Princess Cicely. "
Absolutely not. There is no evidence that Cicely of York had any surviving children (outside of one pedigree which is unsupported by any primary evidence). I really have no idea how you can claim Robert de Welles is not a son of John Welles but is a son of Cicely. It makes no sense, and more importantly there is no evidence to support it. If you are conceding that Robert was not a son of John Welles, then he also cannot be a son of Cicely.
"Linking Robert to John Wells (1537-1618) does not turn on his being related by blood to Sir John but, rather, linking John Wells to Thomas Welles, Baron Welles of Stourton (1515-1558), who appears to have been accepted as the son of Robert. If that link is established, the connection to Princess Cicely is confirmed."
Thomas Welles was not Baron Welles of Stourton – no such title exists. We know next to nothing about Robert Welles of Stourton. We know a Robert Welles was taxed in Stourton in 1523 on goods valued at 40s. That’s it. Nothing else. Thomas was not and is not accepted as the son of Robert. It has been suggested that he could be the father of Thomas Welles who was taxed in Stourton in 1542 based solely on the dates being about a generation apart. But there are no wills, no baptisms and no court records connecting the two men. You are saying that the grandson of Edward IV, a son Princess Cicely, and a 1st cousin of Henry VIII went unrecorded in the primary records, and lived in complete obscurity.
"Googling John Wells will elicit links both to the son of Thomas and to the mystery John in the Wikkitree profile. Both were born the same year in Ringstead and both died there on 25 March 1618."
Googling will bring up no links to evidence based on primary records. Thomas Welles of Stourton did not have a son John born in Ringstead. He did not have a son John at all. The administration of his estate in 1558 shows that he had two children, Robert and Ann who were then under age 21. There is no connection between the Welles family of Stourton and the Welles family of Ringstead.
"If anyone can access the death records in Ringstead, it might show John's parents; or, alternatively, that of Robert -- or his will -- which might give names and dates of birth of his children. (According to findagrave.com, Robert is buried St. Michael's, Whichford, Stratford-on-Avon District, Warwickshire, England.)"
Again unsupported by actual evidence. The earliest burial of a Robert Welles in Whichford was on 29 July 1560. It is unlikely this is the same Robert Welles who was paying taxes in 1523, though it is possible. No will for a Robert Welles exists in this time period.