Well, while her claim was never exercised, she was important. In some ways, with the exception of those people leading Henry's army at Bosworth (Oxford and Jasper), Henry's 1485 usurpation was supported by 'loyal Yorkists', who deserted Richard and his followers. The reason being that there's precious few Lancastrians left. As you say, Henry was a thoroughly political animal. he knew there was no Lancastrian cause left. that's why he pledged to marry Elizabeth all the way back in 1483, when he was crowned in a Breton cathedral on Christmas day. His wife - both as intended, then actual - brought supporters and legitimacy to his cause, which would have been difficult to accrue otherwise.Then why did Henry marry her?
He was a thoroughly political animal, so it's not likely to have been just for her good looks. She clearly brought him enough additional support to make her worth marrying.
He still claimed the throne by right of conquest, though.