Sorry, that account name is already taken
In the long term, I think services which rely on a limited namespace and a network effect will find themselves constantly being replaced by slightly newer instances of the same basic idea. Here's why.
Think about phone numbers. In the US, it's a 10 digit number that can basically follow you around. It wasn't always this way, but portability has changed things. Your "area code" doesn't mean a whole lot any more. Phone numbers get recycled, but for this thought experiment, let's assume we stop doing that, and you get one for life. When you die, it gets locked up and nobody can use it again. The same thing applies if you just get tired of having a phone and stop using it. In this scenario, those 10 digits are locked out forever.
If this were the case, we'd eventually run out of 10 digit numbers and would have to figure out some kind of alternative system. However, long before it was actually exhausted, I imagine people would start looking into other places just because all of the "good numbers" were long gone. Imagine if you found out that you could never have any remotely interesting phone number because people who have been dead for 50 years already used them. That would be really annoying.
Certain services online are getting to this point already, so just imagine what life will be like for them in 100 years. Anyone who's made much of a mark on the Internet to date will probably be gone. Now think about all of the finite resources in different namespaces which will never be recycled. It's all of the things which are currently in use by the entirety of humanity online. Every one of those permanently deactivated account names is just one more our kids and grandkids will never get to use.
I don't know if Twitter allows you to recycle account names, but let's say they don't. Eventually, every single word in every language will be used as an account name. Then all of the compound words which can fit within their length limit will disappear. Then all of the word + number combinations (like "rachel31337") will disappear. Remember, I'm talking 100 years out here. A whole bunch of people will come and go in that time.
What I'm saying here is that long before any of these places hit their theoretical cap on unique names, users will have already found a newer one, and they won't even realize why it keeps happening. It'll just turn out that the latest hangout for this decade's batch of teenagers is a place which didn't exist only a couple of years ago. Some years down the road, it'll happen all over again, and it will just keep happening.
While there are always issues of "coolness" and trying to find a place which isn't well-known yet, I think a lot of this ultimately comes down to being able to stake a claim to your own preferred identity. If you have to settle for some abomination with extra digits and junk characters on service A but can get exactly what you want on service B, don't you think you'll lean towards using B more often?
Once that bias exists, it's just a matter of time before the newest group of users grows into it, and the rest just happens naturally.