The big problem here is in the concept of the time loop, not in our heroes' treatment of it. The loop must be nearly unavoidable by definition, or else it would not exist.
1) If the loop depends on this super-accurate collision with a fellow starship, then it must
follow that the collision is going to happen no matter what course the E-D takes, although perhaps within certain limits. If changes in course were relevant, then the random fluctuations of the loop would preclude the collision most of the time, and there could be no loop. Somehow, the E-D must be a disaster magnet, causing the Bozeman
to pop out of the past at the exact millisecond and location that will result in a collision, regardless of where the E-D herself is and when. Although, I guess, still within the Typhon Expanse... (But the ship isn't allowed to leave the Expanse - her orders are to study it. And if it eats starships, then all the more reason to poke around and make the area secure for further visitors!)
2) If our heroes knew the above, they should not worry about course changes, but they should worry about ways to survive an unavoidable collision. And this is indeed the conclusion they reach in the discussion. However, the heroes in each of the loops, even the final one, are unaware
that there is going to be a super-accurate collision with a fellow starship. All they know in the very final loop is that they are going to die in a collision with something, perhaps an unavoidably large object or entity. That's in some ways even less reason to think that changing the course will change the future - but in other ways, it gives hope, as the concept of a "safe course" might still theoretically exist. The episode as written makes good sense if the heroes assume the collision will be with a small object, though, even if they never voice this sentiment.
3) The heroes don't even know when disaster is going to strike. Today? Tomorrow? Three years from now, as per the mysterious "signs of three"? Stopping to worry, to launch probes, or otherwise prevaricate, is unthinkable in those circumstances; Starfleet officers can't afford to be paralyzed like that. And luckily the episode doesn't feature them immediately springing to rash action; rather, it has the disaster visit them again before there is time to decide between action and inaction.