When you’re on an online dating site (or even if you’re not), you’re clearly going to be dating multiple people. If a girl tells a guy, “Hey, it’s hard to talk on here. Why don’t you take my number,” then she most likely has also said that to 5 other guys that day. I’m not saying she doesn’t like you, I’m just saying you’re not the only one she likes.
If you’re on a site like Plenty of Fish or OKCupid, it usually means that you’re serious about finding a relationship (or, at the very least, someone you’re compatible with and like hang out with). Therefore, what would be the point of seeing a cute guy/girl, sending two or three messages back and forth, exchanging phone numbers, and ignoring the other 400 messages in your inbox?