As well as what ISL said, if the universe is toroidial it seems like it's larger than our visible horizon. While images of an individual galaxy might be hard to tell if they are repeated, we can see enough of the structure of the universe that if our visible horizon was much larger than the real value of the universe and there was wrapping going on, we'd see it. This isn't the exact sort of video I'm looking for, but it's close enough to what I'm talking about: https://www.youtube.com/watch?v=rENyyRwxpHo Everywhere we look we see distinct structures.
It is not a bad thought, though. It may well do some sort of wrapping around, just at a larger scale than we can see. It's an open problem.