Herazeus, the title of duke of York was *not* "always" given to the second son of a "sitting monarch." Frederick was never king, but his second son was indeed created duke of York by his grandfather. George V's father was not a sitting monarch when he received the title.
I'm very interested in the Wars of the Roses --where did you read about a "settlement" about the title from the Wars of Roses?
Frederick's second son was given York after Frederick died and his children had been upgraded such that they sat in a similar position as if they were children rather than grandchildren. Meaning, technically they were grandchildren, but in the light of Frederick's death, they moved into first and second positions in the line of succession thus fulfilling the criteria needed for who holds the title of POW and York.
George V's father was never York. He was Victoria's eldest son and granted POW in 1841, a month after he was born. For the one month prior, he was Rothesay and Cornwall.
Victoria never used York despite the title becoming vacant a decade before she was Queen.
The York settlement wasn't a formal agreement set out in documents. Perhaps calling it a settlement is misleading. It was a series of symbolic acts carried out by Tudor to unify the two sides of the conflicting branches of the royal house that kept the York house visibly displayed to appease the Yorkist faction and maintain their support. To that end, he married Elizabeth of York, he named his second son York, just like the very popular Edward whose supporters he needed, and he created a Tudor Rose emblem that displayed the white rose of York within the red rose of Lancaster.
The reason the Yorkists had to be appeased was because despite winning the crown via battle, the Tudors' claim to the throne was tenuous at best, and from a doubly illegitimate line. The tudors later became masters at PR to deflect from these 2 points.
Btw, as a war of the roses afficianado, have you watched the latest documentary on it by Lucy Worsley?https://m.youtube.com/watch?v=dANvIjbtuDk
To be honest i agree with her thesis because of the available documentation, but also because the 100yrs war supports it too.