I think most understand there's a mental side to the game - I most certainly do. I think the question is how much of a factor it really is and/or how you factor that into your decision making.
How much different is it pitching in the 8th instead of the 9th? Over his career, Hoffman has pitched better in high leverage than he has in medium or low leverage and as Term pointed out, he's pitched best in the 8th, worst in the 7th, with the 9th somewhere in between. How do those results suit your narrative that he lacks mental fortitude? Why would he be worse in the 7th than the 9th if he struggles with the mental pressure of closing?
The reality is the mental side of things will be different for every player in baseball - and it is something that is constantly changing. Players may learn to handle the pressure more as they age and mature, some people go into slumps and lose their confidence altogether.
I think it's also incredibly simplistic to just label someone as being unable handle a certain role. We see players who've failed as a closer for a couple of years suddenly figure it out and dominate for several years. We see players who have dominated as a closer for several years, who suddenly struggle with it. We see closers who are dominate one year, then suck the next, then dominate again. The only consistent thing about relivers is their inconsistency.
The reality is there's really not black or white answer. It's similar to the discussion on lineup protection and whether it exists or not - and if so, to what extent does it matter. Anyone claiming their right and the answer is clear is ignorant.