The downside is that some countries have restrictions on names; in Australia, a .com.au must match up to a registered business, which is awfully useful to prevent squatting when you add trademarks into the mix. No such dice with the straight .com, .org, etc.
(I like that we have both "restricted" and "unrestricted" zones; I can go register beiberloveskittens.com, for example, but know that beiberloveskittens.com.au won't go polluting the .com.au namespace without at least someone going to the effort of setting up a business for it to be attached to.)
I don't think we do. I think 1 global namespace would be enough.
Say we ditched TLD's and limited domain names to 10 alphanumeric characters. That would still be enough domains to give 450,000 to every person on the planet.
That's with just alphanumeric characters capped at a length of 10. Allow unicode and remove the cap and we would have plenty of domains to go around.
All in 1 namespace.
Edit: yes I understand that the vast majority of those domains would be nonsensical, however even eliminating 99.99999% of them would still leave enough meaningful domains to go around the world many times over.
Every particular string may be made memorable, but you'd have to memorize it. Instead of it being natural, as in: a natural extension of how people think about things.
Back in the day I worked for BT and had memorable mail addresses such as 018222211 (Prestel) and 80:BTG174 (Dialcom/Telecom Gold) at least the Telecom Gold ones where slightly memorable as the prefix BTG stood for British Telecom Gold.
It is not my idea, but really, should't we abolish the TLD in general? Instead of http://google.com, http://google.de, http://google.tv .... we would get just http://google .
The reason why we have geographical TLD is just political anyway.