Paper and physical things also convey a lot of information - not just their literal content, but also cultural/social and economic information. When someone spends a tenth of a cent spamming me with some crappy E-mail, I notice. And if someone spends $5 or $10 to send me nicely designed marketing material on nice paper, I notice. I'm not saying that dictates my buying decision - but I know that I'm willing to spend money on marketing if it's to the right person who's likely to do business with me, and if I can tell someone spent real money to reach me or communicate with me, it demonstrates that they're seriously interested in interacting with me.
Nice materials also suggest permanence/longevity and success - I'm pretty wary of spending a lot of money with an organization that appears to consist of one guy with a laptop and a cellphone and a $20/month VPS - because I don't feel very confident that he'll be there if I need post-purchase support, or I want to buy another one of whatever he's selling.
If I talked to someone who said "I don't have a business card but if you give me your e-mail address I'll get in touch" I would suspect that the person wasn't very committed to their business/profession if they couldn't be bothered (or couldn't afford) to spend a little money on business cards. It would make an impression - but not necessarily a favorable one.
Noting down an email address and making sure you've spelled it properly takes time, something that is not always available during a brief meeting in a public space.
What does baffle me is that phone manufacturers have never been able to turn vcard exchanges into something instantaneous and convenient. There's usually always some form of handshake that involves navigating convoluted menus, or else leaving your phone perpetually discoverable and hence open to spamming or worse (for that reason, many devices don't allow this full stop).
