I understand the mortality rate for pioneers along the Oregon Trail in the 1840s was over 30% - as you say, mostly disease and accidents. Of course, there was a 'base line mortality rate' that was experienced by those who didn't migrate, and that rate was probably appreciable.

One thing I have experienced on multi day trips, either climbing or bike touring, is that on about the third day your body shifts gears, so to speak, accommodating to the new regimen, and life becomes more comfortable. Even so, rest days are a good idea. It is a common practice for thru hikers on the Appalachian or Pacific Crest Trails.