It would be creepy even over coffee.
“I’ve been looking at you like this for a while now…”
“And…”
“And I’ve been wondering.”
“What have you been wondering about?”
“If you’re available.”
“Drop it, chev. Every single girl in this town knows… yadda yadda.”
Or, worse:
“What if I am?” (Wiggles and twirls a curl. Upon which you should run for dear life.)
Plus, if a girl’s not a keeper as a friend, she’s not a keep as a girlfriend. (Minor exception when she claims to be a friend while acting as a girlfriend, which is sort of okay when she does actually want to be your girlfriend but not when she actually really wants to remain just friends permanently.)
It’s even more fun when the person who didn’t date all sorts of vaguely not bad people like others did actually does achieve the dream and find someone special.

(Not talking about super model look really, though.)
Well, if I had a so called girlfriend (“boy” and “girl” doesn’t sound right for adults), I would be pleased if she went on dates with guys. She could do that of course, but without continuing to be my girlfriend. And I’d probably not be interested in further participation in any capacity anyway barring someone who honestly admitted taking a step too far and asked to take it back, maybe.
+1. Besides, don’t destroy something which is working.
Actually, those are the qualities which make a woman think you’d be great in her friend zone.
I take a different perspective—may the woman make her choice. I suppose your perspective is female-centric, while mine is a little in the opposite direction.
Now as for “no vows”, sure, a promise is not a vow, but I wouldn’t marry a woman whom I couldn’t trust with a blank cheque or with Brad Pitt in a dark locked room (or a gun etc.). I’d be understanding if she wanted to make sure (though I’d rather be told that openly), not close herself to meeting someone better etc., that’s all right if I’m afforded the same rights as she claims for herself in this regard (and I’m a bit skeptical as to how you would feel if the tables turned in your example, to be honest, that is if a man did the, “may the best girl win,” kind of thing), but if she actually broke a promise, even an implied one, the prospect would probably be dead even if she decided she were more interested in me than in the other guy. Friends don’t do such things to friends and I wouldn’t cast my lot with a woman who were not a friend I could depend on.