Seems like you are pursuing two inquiries: Why do people with ALS experience global fatigue, and why do you feel progressive fatigue during the day?
I don't really know the answer to your first question, but I have been told by at least one well educated person that the answer isn't clear. One common thought is exactly what you stated, that the gradual weakneing of muscles requires the body to work much harder.
Your second question isn't necessarily easier to answer because it depends on what is ailing you. There are a number of neuromuscular related illnesses (like myasthenia gravis) that improve with rest, and it is a good sign what you feel is not ALS.
Best of luck,