What's the value of this?
It allows twitter to easily track which links you're clicking on, which some might consider to be a violation of privacy.
On mobile, t.co makes it so that you end up always launching a browser before launching the appropriate application (i.e. YouTube)
When you copy and paste and send a link to someone, they have no (easy) way of knowing what you're sending them without description or visiting, and it gives Twitter a mechanism for tracking who you send the link to. (One could posit a "malicious" tracking twitter where they serve up t.co links to people which are dependent on the logged in user to track that user's social network... fortunately I don't think this has happened yet.)
I understand the value of being able to track click-throughs and quantify virality or whatever, but there really needs to be a better way to do this.
The fact that t.co don't have global servers probably doesn't help, in Asia and Australia ping times to t.co are 250ms+. Even in Europe it's over 100ms.
That's what URL unshorteners and/or Link Bubble (which automatically redirects to apps for you) are for.