So, no. This doesn't tell us anything about the possibility, it merily tells us, even if it _was_ possible, we're collectively to stupid yet to deal with it without destroying our future which would've led to inventing such a device.
It is entirely plausible that the universe limits your interactions with your past causal self to a small range, allows arbitrary overlapping world lines, blocks all causal violations entirely, or has disastrous consequences for time loops.
My personal bet is that the universe has no reason to care that you've interacted with your past self given a consistent proper time worldline. This however removes conservation of energy and momentum in the universe, which General Relativity also does not preserve.
Of course this does allow for misuse of causal loops to generate arbitrarily large/infinite amounts of energy without any bounds on observability.
Who says science can't fill the soul with wonder?
[1]: https://link.springer.com/article/10.1007/JHEP12(2017)151
Wormholes can be turned into time machine in the following way. Remember that time travel to the future is pretty trivial: Just accelerate a lot and enjoy the effects of time dilation. So in order to travel into the past, you create a wormhole pair and put one of the wormholes on a speedy two-way trip. If you now traverse the wormhole that was on the trip (and which has traveled into the future), you travel backwards in time. But not further than when the pair was created.
inspirational quote: "Your future self is complaining about how much time you waste"
person: i'll show him! i'll ruin his f**ing life!