In my experience, girls do want first and foremost an alpha male, and being a nice guy on top of that makes it even better. It's just not a necessity so the jerks can succeed without that quality, whereas the nice guys can't succeed without "dominance."
I'm sure you have friends who you would consider incredibly nice, but very shy, guys who never could get a girlfriend, and plenty of jerky, but confident, guys who you wonder why girls would date. Confident guys, even when not nice, just seem to win out over really nice, but not at all confident, guys. Guys with both win out over both. Whether or not it's a bad thing is your call.
(I'm not arguing guys are above their primitive desires: not by any means, it's just not the focus of this discussion.)
I guess now we know what time_management's new nickname is...
The antonym to strong is weak, not nice. I think people often forget that girls, particularly sane and intelligent ones, do not reject the prototypical "nice guy" because he is nice but because he is a pushover. That is, weak. You can be strong and nice. In fact, I think the strongest ones usually are "nice" or considerate because they can afford to, whereas at least where I'm moving, being an asshole or abrasive is a sign of weakness.