On second thought, maybe men don't want to be your "friend" as they do not find the proposition of a vague, shallow, and meaningless involvement in your life particularly intriguing. That is all you appear to be offering, and it's not really going to snag you anyone with having.
I mean we're talking:
A- Fools, imbeciles, and low-lifes who won't mind being used as playthings,
or
B- Abusers, sadists, megalomaniacs, mid-lifers, etc. who just want to use you as a plaything,
and possibly also
C- AIDS
or
D- an unexpected fetus
PS- "Independently wealthy" means having enough in capital, assets, and investments to live comfortably without having to work. It does not mean just having a high-paying job.