I thought the point was that Twitter can add a few lines of code that check whether a URL is shortened before re-wrapping. Fewer redirects, less time till I get to the real content.
They probably don't want to completely undo other shorteners, however, because these services aren't only used for shortening. I absolutely believe it's beneficial for them to have multiple levels of indirection so others can gather stats, I just don't like it as a user who is consuming the links. If the amount of indirection, delay in loading pages, and brittleness of links gets bad enough, maybe it eventually will make sense for them to try harder to avoid it.
But they could, in some cases, avoid increasing the amount of indirection and still gather the same stats. For example, on their site, since they open links in a new tab anyway, they could make that link direct and capture the click event with a separate AJAX request in the original Twitter tab.
If you focus only on page load latency, other sites/services besides URL shorteners are making things worse. I regularly notice some small delay waiting for my click on a Google result to go through Google's servers since they (annoyingly, in my opinion) swap out the target URL for a wrapped version at the last minute. Of course, Google has other good reasons for doing this as well -- stats and removing referral information immediately come to mind.
I also didn't show that this negatively impacts user experience. It could be that t.co, on average, requires so little overhead that the extra level of indirection doesn't matter. But I think it's worth looking into, and if it does have a negative effect, figure out ways to mitigate these effects.
On mobile I notice the slowness of t.co a lot. On desktop I have been noticing waiting for the google redirects too recently. So I think they are a problem, but potentially more resources thrown at the problem could fix this, but using other means would be better as you suggest.