No, it's because of the bikini scene in "Planet of Fire." Or the pink leotard thing in "Attack of the Cybermen."
In short, I really think that Peri is beloved as a character wholly because of her sex appeal.
I think she's a better realized character in Robert Holmes' scripts ("Androzani," "The Two Doctors," "The Mysterious Planet") because Holmes wrote her as Sarah Jane. (Quite literally so in the first case, and in the latter two cases I can "hear" Lis Sladen saying Nicola Bryant's lines.) In Eric Saward's scripts, though, she's written with few redeeming features.
In the tie-in fiction, I think she's popular because she's such a blank slate.