FWIW, this is similar to the reintroduction protocol my registered dietitian used when I did an elimination diet through my doctor's office back in 2006 after food allergy testing. As I recall, the rationale for having the food in question at all three meals was to be sure you ingested enough of the food group to conduct a sufficient test for sensitivity. If you feel crummy after 1 serving, that might be enough to stop. If you feel fine after one serving or you're not sure, it's another good reason to have the item in question at all three meals (or, if you have unclear results after 1 day, add another day of testing said food group).
EDIT: the order in which you reintroduce food groups doesn't matter. The Whole30 reintroduction schedule is a sample of one possible order.