Actually, planning rest days allows you a great deal of built-in flexibility if you are taking a longer tour.
(They really don 't apply as much for short tours.) If you have plotted out a route that requires 75 miles per day - every day - and anything goes wrong, then you miss your flight back to Peoria.

Including at least one rest day per week allows you to chill out at that beautiful campsite with the people you have just met. It allows you to do a half day and quit in a nice town or park that you didn't know about. It allows you to spend the afternoon at a bike shop without freaking that your "schedule" is getting totally messed up.

I have done many 3000-5000 miles trips. I usually do about 400 miles per week in summer - less in winter with the shorter days. That usually translates to 4 full days, 2 half days, and one day off. Like most touring cyclists, I like to tour the spectacular scenery - - so why not get out and hike in it? Like Yosemite or Grand Canyon or Denali?

PS - Of course, Nancy, I'm not sure if you have ever taken a "longer" tour. Hee-hee.