Wherein I argue that the answer is no:
https://25yearslatersite.com/2018/05/04/the-time-travel-trial-should-cooper-have-gone-back-to-1989/
Not to be glib, but I do honestly subscribe to the idea that there is no 'if' or 'should' - every action always has been and always will be in the totality of space-time. Not many-worlds, but this world. It's a lot like a tv show, whether you've watched it or not, whether you plan to watch it again, the actors always make/made the same choices and always will. Larger than the tv metaphor, I think it's how existence really is.
Time we like to think means the future is unwritten, but just like you can't know what's over the mountains until you walk over there to look, you can't see what's in the future until you wait over there and look. But it was always there.
That could be a consistent view when it comes to reality, certainly. If I don't ascribe to it, that would be because it seems to leave no space for freedom. I guess I am committed to the existence of metaphysical freedom in some way, personally.
When it comes to Twin Peaks, though, your position is interesting to think about, but not something I can make consistent. Rather, Cooper's time travel creates a paradox, which was the central point in my position here. I tend in the direction of a many-worlds interpretation to make sense of this and a number of other things in the show. I do not necessarily endorse the many-worlds hypothesis when it comes to reality/physics.
But we're supposed to be talking about Twin Peaks. So, I wonder, how do you interpret the time travel and so on, if you want to say there is no "should"?
I think there's possibly a compromise to be had between you two splendid gentlemen's views, at least as applied to The Return.
To take Joseph's view, that what will be has been, or what has been will be - take your pick - I think The Final Dossier backs this up. Laura is removed and the timeline altars, and yet it doesn't; Laura doesn't die but she disappears, Leiland still dies, by suicide too, although this time it is a year later out of sorrow for the loss of his Daughter. And lastly, Cooper still comes to town and once again disappears (it is fair to assume Coop has once again found his way to Glastonbury Grove).
So the same things, at their essential level, still happen. But the form these things take differs slightly. The future is already set; you can mess with time, but time will still find its way on the course it has set.
Where Cæmeron's questions of free will and agency come into play are where Coop's attempts to change the past have potential to be successful. Imagine if he reached enlightenment, lost his hubris. He reappears back in Peaks in 89, but remembers his many past efforts and this time understands to let Laura die and be redeemed. He doesn't enter Glastonbury Grove and manages to leave Peaks still himself - would time allow this act of agency? Would such an act only be possible by becoming enlightened and recognising that this is not the first time you have lived this life - only then would it be possible to break time?
Nice. My shift is almost over, so I'll have to read this tomorrow night.