If Gowasu can really travel to future at any point of time, why didn't he foresee Zamasu turning rogue in the first place?. He could have foreseen this even at the time of choosing Zamasu as his apprentice?
NOTE: My answer is now complete. Thank you for your patience while I edit.
To answer your question, there are a lot of context clues given through the dialogue in each episode. I will point these out then list my answer below.
What we know
When Beerus found out that Bulma built a time machine, he mentioned that time travel or tampering with the future is highly forbidden even for gods, and that he should destroy her right now for committing such a great offense.
This proves that gods have knowledge of time travel and have rules in-place for protecting continuity of the timeline. Also, he never scolds Whis for using time manipulation twice (once against Freeza and once to save Gowasu in the present), also proving that angels do not follow the same protocol as gods and humans.
Gowasu takes Zamasu to a distant planet to observe a human-like species in development. He scolds him for killing a human once they went a few thousand years into the future because Zamasu committed an action that could have changed how that entire species would develop.
This proves that gods are forbidden to travel unless certain circumstances arise, but are also expressly forbidden from interacting with things in the future or past.
Zamasu and Black both state in the battle with Trunks (the specific battle was the one where he transformed into a hybrid of SSB and SS2) that it is because of Trunks's actions during the Cell/Android saga of jumping back and forth through time that really helped them come to the conclusion that humans need to be destroyed.
With those 3 key pieces of evidence, it is very apparent that gods can time travel and they can do so at will, but they MUST exercise a great deal of discretion and restraint when doing so and should only do it under certain circumstances.
Gowasu could have looked into the future to predict his death, betrayal and all of that, but if he did he would have arbitrarily taken actions to protect himself and changed the timeline which was forbidden. Now maybe he knew that and maybe he didn't.
However, Gowasu has stated that the role of a Kai (God) is to observe. So I highly doubt he would ever look into the future. His whole reason for even using the time ring the one time that he did was to prove a point to his student.
So in short, yes, Gowasu could have gone ahead and prevented Black's existence. But if he did, it would do 3 things:
- Contradict his character
- Ruin Black's existence
- Make the current story arc (which I find very entertaining) disappear entirely.