Personally, I don't think a character who really wants to kill someone, and is being hyped uped necessarily looses any personality if it were to turn out he couldn't beat a character who's being downplayed. Exactly what character development would he be getting if he actually got close to killing Luffy anyway?
There's only two things about Caven character: he's a strong swordsman, he hates the rookies from 2 years ago. With
Rebecca on the other hand is a princess who wants to help the one who have raise her by taking out the evil boss.
Rebecca haven't show anything that puts her on a NW level strong while Cavendish is wielding Durandal and stopped Chinjao on his track.
Rebecca have taken out by Luffy busy eating while usually he is a way to show how well a character can fight. Cavendish while not getting the upper hand on him is still keeping a good performance when face with him.
In the end I think that Rebecca doesn't need to be weak but simply needs to be weaker than Cavendish. Cavendish needs the hype he gets so that he doesn't turn into being ridiculous agaisnt Luffy or the others from two years ago for the matter. He gets to be love because he's both a show of strength (fruitless swordsman doing well in NW) and a comic relief(kill the ex-rookies).
Rebecca is appreciate for her backstory and determination. And the maximum of strength people required from her is the one need to take down or put a good against Dofla's minion. Not necessary to beat Caven to achieve that.