We use the kitchen in a 1BR (or larger) quite extensively. In fact, we use it to motivate our park time.
We pretty much always rent a car for the stay, but we have used the grocery delivery when not renting. This makes it convenient to get the groceries.
As for our plan:
All breakfast (except one character breakfast) is eaten in the villa (usually cereal, eggs/sausage-bacon/toast).
We use lunch as a motivator to leave the parks from morning touring and ensure we have afternoon downtime. Thus, we will eat most lunches in the villa (sandwiches, leftover dinners).
Finally, we nearly always eat dinner in the villa before heading back into the park (usually easy prep like spaghetti/pasta&sauce, casseroles, heat & serve frozen meals, burgers & fries, etc).
As an aside, we also use the kitchen to store/prep snacks in the park and celebrate special occasions (birthdays, holidays, anniversaries) with a small gathering of family/friends that come to visit (I'm from FL). Usually, this involves cake, special meals, etc.
Other thoughts:
We actually save quite a bit of money not using the restaurants at WDW, and this becomes even more of a psychological thing, as we feel the quality has dropped a bit and prices risen over the past decade or two.
The kitchen and washer/dryer are the true "best kept secret" about
DVC. Both are indispensable for us, and we are always happy to have them at both resorts (WDW & DLR).
A final note...
The kitchen is even more important for families with food allergies. While WDW is a safe place, for the most part, it would be comforting to know family members can have the same food as at home in WDW simply by visiting a supermarket or using a grocery delivery service.