The male friends I had when I was young and single were not my type. You are right about that. I was involved with a guy for a couple of years and developed feelings for him, and we did remain friends for many years after I met my first and current husbands. I do think it wouldn't be possible to remain friends if one person continues to have feelings for the other after a breakup.
Regarding a man never being friends with a woman he finds passable, you sound like my husband, and he was only right about that once (I still do keep in contact with this guy, persistent as he is). These guys stick around even though I'm married because I am genuine and a good listener. They approached me in the first place because I'm not an uppity-looking snob, like a lot of women are. I have a smile for everyone with whom I make eye contact, male and the few females who don't look like they're better than everyone else. They are comfortable with me right away and talk to me about anything and everything. I keep telling my husband this is why they want to get coffee with me, and he laughs and says I'm naive. I've always preferred being around men because there's no drama with them. Women I've known suddenly act like they don't know you out of the blue and ignore you. Men never ignore you, and they're easier to talk to. That's been my experience.
You know what friendship is, Hellouser--caring about someone, checking in with each other, helping each other out, listening to each other and knowing that person, whether you talk once a day, week, month--whatever--will be there for you in a heartbeat if you ever need anything. One of my BFFs is a guy who used to be my neighbor. We hit it off right away, and when I think of someone I'd lean on if I ever needed anything, he's the first person who comes to mind.