There's no explanation for it. My love of Nancy Drew mysteries is irrational. But there you have it.
I've read this one, The Mystery at Lilac Inn (1930) numerous times. I knew a third of the way through the first time who done it, so it's not the mystery. It's certainly not the racism, sexism, and ethnicism. (There are slovenly Italians and Irish in most of these books.)
It must be the roadster, her frocks, the fact that she
wears a hat and gloves whenever she leaves the house. The plucky girl falls back on her extremely influential father only rarely, but of course it's nice to know there's untold wealth and political power there if you need it. Part of the charm is that my book is the original 1930s edition.
No accounting for my love of these mysteries.