They would, but the causation issue you bring up has a lot of merit in this discussion.
To try an answer to the OP:
Any method proposed to move backwards in time always involves at least one brand new physical hypothesis that has absolutely no evidence to support its existence.
That doesn't make it impossible. However, these new hypothesis proposed are always of the most extreme nature. To make a wormhole, you'd need matter with imaginary mass. Moving one of the ends seems quite unlikely. Nothing with mass can pass the speed of light barrier (whether they were slower to start with, or faster). There is no exception to that rule currently, and it is unlikely we'll find one.
Many times betting against science is a losing proposition. This limitation, however, seems likely to hold for far more than our lifetimes.