if you couldn't have your chosen resort-would you still go on vacation? Would you/do you have a backup resort?
For us the resort is a huge part of our WDW vacation. It is not just a place to sleep. It is a place to sleep, to shower, to lounge, to reflect, to plan, to take in the view, to eat, to swim, and to get to the parks from. The quality of all of those experiences impact our trip in a big way.
The Disney resorts in particular each have their unique style and charm, so that staying at a certain resort colors your trip. I can't think of the first WDW trip I took with my son in 2009 without also thinking of Wilderness Lodge. I was awestruck at the grandness and theming of the lobby, and I remember walking through the tall trees to and from the boat dock on Magic Kingdom days. I have similar resort-specific memories for every trip. Just grabbing a generic motel room on the local highway would not have provided a comparable experience.
So yes, our resort matters. I like many of the deluxe resorts, as well as Fort Wilderness, so it's not like if one resort is not available, we won't go. But we won't stay just anywhere- I always put a lot of thought into it.
You can have a great Disney vacation even if you don't get an ideal resort. One of our nicest trips was the February we stayed at Pop Century. But the specialness of that trip had to do with other factors besides the resort, which itself was not a great place to hang out. Going back there at the end of each day was a bit of a downer. I don't plan on staying at a value again- would rather get a nicer offsite hotel. But if you're asking, "Can a family have a great trip without spending a fortune on an expensive resort?", the answer is yes.