The reason people "tire" out is that they are stuck in certain neuromuscular, movement patterns that they can't get out of and end up fighting with compensatory movements. These patterns also happen to desensitize you to even "noticing" all those subtle torso adjustments and their necessity by using a strategy of over-stabilization in a single sagittal plane at the cost of movement in frontal and transverse planes.
On boy do those movements take a lot of time and dedication to untrain. I've spent the last 2-3 years working on the near constant tendency of my left hand toward ulner deviation. Finally, I think I have it pretty much licked. It took a lot of effort though. Unfortunately, more than most pianist I've met seem to be willing to invest if they even happen to be sensitive to the issue.
The reasons why this process can be difficult is highlighted by this quote from by Shirley Saharmann:
"Faulty training only accentuates the muscular and neurological contributions to habitual imbalance. Most often the faulty movement patterns are an exaggeration in one direction of a limitation in another direction."
The underlying implication here is that you have to get people back into a more "limited" state first before they can retrain the proper coordination. This has its own set of difficulties. But of course it's all going to be for naught if you don't find the correct coordination because you'll just end up going back to the faulty movement. I'd also like to emphasize the word "direction" in the above quote.
Translating this into more piano friendly terms, people will first need to identify (easier said than done) and give up all the mechanisms and strategies they are using for "accuracy" or even "expression" before they can even begin to replace it. Most pianists will refuse to do this because removing all traces of compensation requires returning to a state where they'll question how one can possibly even play at all with any semblance of control. One's skill at doing this entire process correlates with how well one can essentially re-write muscle memory. Again, a respect for "direction" is critical to doing this. More time spent on that word (as well as related words such as "orientation" and "timing") and less on body parts would probably do the piano community a world of good.