Like wars erupting over FTL rather than sharing it, because the country or a corporation who would be the first to have such technology stands to have the potential to colonize distant planets.
Actually there is. The issue with that proof is that is assumes that local arrow of time for the thing you're sending back goes forward. This is just an assumption. There's no proof that it does.
In other words: If your local time goes backward as you travel back in time, there's no paradox since paradox causing information will just unwrite itself from your brain as you get younger.