Endurance is not disputed. We understand the bottlenecks of physical endurance, but mental bottlenecks are is still poorly understood. That study rejected the ego depletion hypothesis for mental fatigue.

I have chosen a poor example and formulated my question in a misleading way. I do not work physically and I am more likely to lack willpower when I am mentally tired even when it is related to other things than physical exercise - for example I am trying to reduce my sugar intake and I am more likely to just give up eat some chocolate after a tiring (mentally) day. That is what I thought was the kind of obvious thing - that when people are mentally tired they tend to just watch a movie instead of originally planned language learning. This is what's disputed?

I am asking because either I do not understand the ego depletion concept or something that seemed really obvious to me is disputed, which would surprise me.

Just speculating, but could it be that your mind is grasping for an explanation, came up with the ego depletion idea, subjected it to a reasonable amount of questioning to ensure that it wasn't completely flimsy, and then you went with it? Kind of a "thinker thinks and prover proves" type mechanism?