I look at it more like, there are certain events that will happen. Lets take the classic, killing hitler before he becomes the ruler of germany. It doesnt matter that you prevented his parents from knocking boots and he was never born, there was always going to be "A" hitler. He might be born a little later, he will have a different name, maybe he will focus on a different group, but World War 2 is inevitable and it will be started by a hitler type of person. For all we know, switzerland may give rise to a man who despises the very idea of watches and wants to lead a holy crusade to purge the planet of timepieces. An unfortunate case of national lead poisoning turns the populace into lunatics willing to go along with it, and the war begins.

But thats why judgement day is going to happen and it cant be stopped. You can stop THAT judgement day, but it is going to happen somehow, some way. Lets say they managed to destroy every piece of future tech that kick started judgement day, wiped all computer records, etc. Unless you kill every person who had any knowledge of the project and anyone they might have talked to, the IDEAS created by seeing what was possible will remain and the robotic future will move onwards. It will happen a little later without anything to use as a stepping stone, but it will happen. Even if you DID purge everything and everyone connected to it, we still live in a world where people try to develop sci fi technology. Eventually, robots will happen. Eventually ai will happen, eventually, that ai will trigger judgement day. And someone will rise to lead the fight back. Maybe the time travel loop will also happen again, maybe not, that part isnt whats important as such, judgement day is whats important.