30s to 1 min break is going to have very minimal physiological difference. I could see the argument that mentally, the single rep and grinding it out without a break could have some value… but most climbs of that duration will have some relief at some point, even briefly.
Now if recovery gets to 5-10 min there’s a definite difference. But take your 30-60 seconds. As you mentioned it is a lot easier to manage when on the trainer!