What speeds up also needs to slow down.
Maybe I'm missing something, but surely the test vehicle will have to stop, and if it fails to stop on it's own, there'll will need to be a way to stop it without killing the occupants, whether these are just guinea pigs, or guinea pigs of the human variety. How on earth can this be achieved on a track only a mile long?
Add to this the fact that the technology is likely to result in an acceleration that is totally pants (a technical term that I'm guessing Mr Musk will be familiar with).
And the result I'm predicting will be some rather embarrassingly slow tests. Or a decision quite soon to spend a few millions on a longer track.