Can Boys and Girls Really Be Just Friends?

A long time ago I was talking to a friend. He told me he thought it's impossible for guys and girls to be just friends. If a guy and a girl are friends, he claimed, one of them likes the other one at least some of the time and usually they are both toying on and off with the idea of dating. I vehemently disagreed, and just to prove my point, we promptly started dating. (Bless my heart).

I went with a friend to Michelle's wedding reception. (Remember Michelle? From the snowshoeing debacle?). Said friend is charming and fabulous, and of course, after he left, it got me thinking about the whole idea: Can girls and boys be just friends? 

Once upon a time I told myself there were two categories of boys:
1-those I date
2-those I'm friends with
I told myself that the two categories couldn't overlap. I probably decided this shortly after JB broke my teenage (20 year old?) heart. I'm sure my reasoning was very well thought out and excellently articulated, but maybe, it's not as good an idea as I originally thought.

I've spent all this time dating boys who were collectively and/or individually
tall, ambitious, funny, charming, talented, flirtatious, athletic, and completely wrong for me.

Wouldn't it make more sense to date the attractive, fun boys who I already think are fantastic? The ones who it's easy to talk to and banter with? The ones around whom I can be completely, totally, 100% myself?

How is this a bad plan?