As you say, it's hard to keep a strong rouleur from getting in a break when they are determined to do and so many riders are going off the front. I think the point many have made is that the mistake is letting that break go out to 10 minutes when UAE has the strongest team in the race (mostly climbers yes, but strong nonetheless). It was never a sure thing that Van Aert would get to the top of Finestre before the leaders, and wouldn't have been able to if starting the climb with only a 4-5 minute gap.
I dont think putting their guys to control break or pace the peloton on the front for most of the stage before the climb would have been really wise either. It wasnt their plan going into the stage and they didnt have the strength to control Van Aert from not going in it. Or anyone else for that matter.
Their tactics was most likely to have the team pace on Finestre for as long as they could, as that would have also been to the strength of the riders they had left in the race. So you let the break go by a lot, to focus on your strengths later in the stage. I cant really knock that approach going in before stage and not knowing the outcome.
However, EF and Carapaz had most likely identified this and made sure to crush that on the beginning of the climb. That UAE wasnt gonna be allowed to dictate the pace for most of the climb. So they went all-in very early, which nobody had really predicted.
UAE just didnt foresee or thought EF and Carapaz would be that bold to go from the bottom, I believe. Something that is out of their control.
Had they known that they might have played it differently, but we will never know that.
All of the above is the perfect storm for Visma and Yates being very strong on Finestre. Because their plan was mostly likely to have Yates attack at some point on Finistre and had put Van Aert infront to be able to help later. Either to increase the gap or perhaps assisting Yates to come back, if that would have been the case.
They also didnt know EF was just gonna throw the kitchen sink in at the beginning of the climb. That Yates was able to ride away from the others and distancing them with a huge gap was dreamland. The cherry on top to have Van Aert stationed as neatly as he was to cruise to victory.