Brad Templeton makes an interesting point about how letters have persisted on phone keypads even as we move to the future and IP Telephony. In fact, courtesy of text messaging their use is growing, even though it necessitates a dumbing down of vocabulary. "See you later" has been reduced to "c u l8r" in a grammatic aberation.
We have become accustomed to years of dialing phone numbers. As Brad points out, there have been mnemonic reminders such as Pennsylvania-6-5000 and 1-800-FLOWERS, to help people remember the numbers. So it seems it may be difficult to give it up. However, without thinking about it we all essentially dial 12 digit numbers all day - IP addresses. They are merely masked by domain names which refer to those IP addresses, in the same way that we think of 1-800-CALL-ATT. Perhaps everyone could have a domain address for their phone. As number portability becomes more common, we could all have one phone number, or domain name, for life, and that number could be automatically forwarded to the nearest handset. Or we could all carry a personal cell/smart phone.
As for remembering those doman names, is there anyone left who doesn't have some sort of name/number storage or address book functionality on their phone ? Certainly cell phones have a wide array of address books, meaning that storing ever more complex information like domain names won't be a problem. In fact, if you've called me, I probably have your number. The biggest issue I can see is that as a result of the disposable nature of cell phones we will need to be able to move that address book information from phone to phone easily. Current phones don' t seem to integrate well with any of the software I use to manage contacts. Hopefully someone is working on that problem.
So the phone company would just become a voice network service provider equivalent to your internet service provider. Maybe they're the same company, or maybe they aren't. And when everything is VoIP, maybe it will be a whole new kind of provider.