You do realize that there is a HUGE combination of characters you can use to create a name, right? Even if you do 1337speak and yada yada, it's massive! To give you an idea, the rules for an Xbox username is 15 characters, Aa-Zz, 0-9 and space. It cannot start with a number or start or end with a space (if Xbox live doesn't take into account case sensitivity, which I don't believe they do). This means for each of the 13 middle chars, there are 37 different characters they can be, the first can be 35 different characters and the last can be 36 different characters. Doing the 5 AM math, that's 35(3713)36, which comes out to be about 1.940472*1019, or about 19,404,720,000,000,000,000 different possible usernames, before the ToA restrictions and already taken usernames of course. Even though you said there are about 48,000,000 million members on Xbox live right now, that barely scratches the surface.
If they decided to go to a UID system, it'd be a catastrophe at this point though. Minecraft did it for a multitude of reasons, but they don't have the player base that Xbox live does. Microsoft has gamertags integrated into the very foundation of their operating systems now pretty much. It would be a huge, costly and resource demanding undertaking just so a couple people can have "Dragon" as a username.
If Xbox live went to this sort of system, it'd be similar to the new city Facebook scenario. You move to a new city and meet a nice person named "John Smith". After you go home, you search for them on Facebook. You don't have any mutual friends with them, so how are you going to find someone with a pretty generic name such as that? Now think of it as you met someone on Xbox live the other day with the name of "xX420N0SC0P3Xx", if you're a CoD player, you've seen a lot of variations of these stupid names, but they're out there. Since Xbox Live doesn't share their personal name,
Now, for the fun math time! Say we wanted to give a UID to each person, we'd have to take those usernames and convert them to a base ten system to store. When you do that, you'll have up to a 24 digit number to memorize to share with your friends, which they would hate you for. You could have a digit up to about 234313593695870215791912, that is using the max character length and highest base value following the original rules that Microsoft has in creating a name (again, before ToA restrictions such as banned names and phrases).
So I don't know about you, but I don't want to say "my gamertag is 'Diggity Dawg', but you need to find me by my UID, which is 9869256294864852!" The average person would space out after the first six digits!
TL;DR: I did the sleepless math on gamertags. We're not going to run out soon. UIDs for the purpose of having "unique" names is a bad idea and not worth the overhaul Microsoft would have to do. Good night.