I suppose it really depends on where you live on whether a car is neccesary.
I'm from the Netherlands, and not even from the big "metropolitan" area (Randstad; Amsterdam, The Hague, Rotterdam) but all things considering I can manage fine with public transport. Yes of course, it's harder to get your date home at 3 at night and you probably would have to ditch him/her at the station at 11 in the evening, but I don't know if that's really much of an issue. If it's a practical matter I would hope your date sees the relevance there as well, otherwise I would really wonder if such a date would be right for me if (in my case) she wouldn't even comprehend this.
Besides; looking at the financial aspect, but that is regardless of the dating issue. I'm quite sure if I owned a car I'd spend more on being mobile than I would on public transport now. Some months I don't even leave town, thus my travelling fees are 0. Good luck convincing the companies that you didn't drive and don't want to pay insurance or other taxes (let alone maintenance that's, at least here, mandatory every year.)
That all said; do I know how to drive? Yes. Do I have a license? No. Why don't I have a license? Because of the silliness that's called regulations. I can't drive a car safely among the mass hysteria that's called traffic and peak hours, though driving a car on a track is a different matter...