would be concerned, for one, that a girl who felt the need to do online dating would not be outgoing enough to be a good match for me.
Your concern is misplaced. Most of the women I went out with via that dating site were very outgoing. My wife is extremely outgoing, as am I.
For some reason, I think that people have the impression that the people who use dating sites are meek, shy, quiet, awkward, loner-types, afraid of interaction, etc. This is all the furthest from the truth. Sure, you will find some of those types of people on dating sites, but it is not the usual or norm.
Most of the people who use them aren't socially awkward people who don't know how to ask others on a date. They're people who are doing everything they know to cast a wide net in order to meet as many people as possible.
I find it kind of ironic when people who are very involved on an internet forum and have never tried a dating site can't see the benefit in using dating sites to meet more people. *shrug*
Edit: Also, I think that people may not fully understand how these dating sites work. The one I went on was pretty simple: you enter in search terms, and a list of profiles appear. I usually just searched using an age range and my city- I knew that there were women I wouldn't date for being too young, and those who I felt were too old for me. Or, you don't enter any search terms at all, and you see a list of all profiles in your city.
I think people are under the impression that the dating site will use a formula of some sort to match only certain people with you. I'm sure that there are some sites that do that, but I'd bet that there are more that work the way the one I used worked. It's still hit or miss- someone might have an attractive profile, but once you meet them, nothing. But it's hit or miss if you ask an attractive girl out who you met at a coffee shop- she might look good at the time, but once you're on the date, nothing.