I volunteered my office e-mail and phone right away, as I will get those all day whereas I would have opportunity get on a dating website only a couple of times per week. Keep in mind that many people can not, or will not, use dating internet in their work place, but may be able to access Google and others that have free e-mail.
Also, as others mentioned, technical difficulties can impact eH. Formatting options and features tend to be greater, too. I really like having “reply with history” when I use e-mail, especially if I had more than one communication concurrently or we were “conversing.”
Personally, I favor a direct, straightforward woman, and I have had better success with women who divulge their personal contact info sooner. My experience in this area is that there is a large difference in the probability of an actual meeting and our ultimate actual compatibility between those who “hide” and “want to build a relationship over e-mail” versus those who step up, take it to the work e-mail, and then, you know, go on a date!