True, but it wouldn't be the first time an illegitimate daughter of an English king was used to solidify an alliance with a minor prince or king. Think of Henry I's daughter Sybilla's marriage to Alexander I of Scotland. And John's daughter, Joan, was married to Llywelyn the Great. Come to think of it, Henry II's sister, Emma, was also married to a Welsh prince.
Plus this alliance would just be fun. If Elizabeth was in Sweden when Erik lost his marbles, then she'd have given the would be John III and the Swedish nobility a run for their money.
But, more seriously, there was a lot of talk during Henry's reign of Elizabeth marrying the Earl of Arran. Even without Edward and the "Rough Wooing", this match would still have advantages.