One thing to keep in mind is that email is not synchronous, so you can get an email and just not reply for a while. Of course you can ignore phone calls, but it's not the same as ignoring an email. Additionally, phone numbers are useful if you don't have access to data, for some reason, or need to contact someone in an emergency. As a counter to your point about remembering phone numbers, I don't remember most, but I remember very important ones (like my father's).

I would recommend knowing one phone number of a person you trust. Type it in when you call them and you will remember it in an emergency. If you get into a spot where you don't have your own phone and get to make one call, you will be very happy to know a number of someone who will help.