As I understood it, this pertains to a specific implementation of a time machine i.e., the Gott time machine.
The jury is still out on other implementations, though of course everything seems to point towards them being impossible.
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You're right, but what other implementations have proven they can actually produce a closed time-like curve?
Well, you have wormholes (but they require exotic matter) and anything with singularities in it; there is the Gödel solution of a "rotating Universe" (which could be true for a "parallel" universe), the van Stockum's solution and so on.
I guess until closed time-like curves are proven to be unphysical (which seems likely), physicists will keep coming up with possible solutions to Einstein's equations which allow for CTCs (and refuting them). And who knows, maybe one of them can be implemented by humans.
On the other hand, it would be very interesting to know what is the mechanism by which the Universe protects itself against CTCs.