Just thinking more about the idea that members of House Stark and House Cassel would not marry each other. Isn't the pre-Aegon's Conquest House Tyrell kind of similar to Houses Cassel or Poole in that they're stewards of Highgarden (thinking of House Tyrell like the Pooles and Cassels is kind of helpful is understanding why the other Reaches Houses were so upset upon their elevation). Yet even then daughters of House Gardener (unsure on sons) seems to have marrying into House Tyrell, no?
I don’t know that I would equate House Tyrell and House Poole, simply because we know too little of the Pooles’ history to compare. With the Tyrells, we can see that, almost from the beginning, the Tyrells are in positions not simply of stewardship, but closeness to the ruling House and even (on some occasions) power and influence. The first Tyrell was Ser Alester, an Andal knight who became the sworn shield of King Gwayne V Gardener - a position which would have required near-constant attendance on the king, keeping his counsel and perhaps even being asked for his thoughts by his royal master. It was under Alester’s son and grandson that the Gardeners formally made House Tyrell the High Stewards of Highgarden - an official, hereditary position for the family in the royal court. Indeed, Yandel emphasizes that “many [Tyrells] became close confidantes and advisors to their kings”, and were trusted with considerably authority. A nameless Tyrell served as regent for King Garland VI, while Ser Osmund Tyrell led a coalition of 40-odd reacher Houses to end the Manderly-Peake Civil War (which really needs a better name) and installed Mern VI as King of the Reach; it was, in fact, because Ser Osmund, his son, and his grandson ran the kingdom for Mern the Dummy that Ser Robert Tyrell was given a Gardener princess for a bride, with “nine more unions” in the following centuries.
This isn’t to say the Pooles couldn’t have had anything like this in history - but all we know of them is Vayon and Jeyne. We don’t know that House Poole ever held the title “High Steward of Winterfell/the North”, or if indeed the office of steward is hereditary with the Pooles, and certainly not if any Poole ever ran the Northern kingdom/lordly realm the way the Tyrells did, or were granted a Stark marriage. Maybe; but without knowing more, I’ll stick with thinking of the Pooles as landless minor Northern nobles.