As a family with two teachers and a school-age child, we have NEVER been able to travel any time except peak. Christmas, New Years, Thanksgiving, Easter (a few times), mid-Summer. We have been in the parks many times when wait times get like that. I don't think we have ever NOT gotten to do everything we want to on any given day and we have never waited more than 45 minutes for anything.
If you plan extensively, you can do a lot even on the insane crowd days. NYE a few years back, we got to Epcot at opening, did 3 rides, then camped out in the pub at Rose and Crown. We sat and played cards, ate, drank, met people, met more people, left to use FPs every once in a while. Then outside in the evening to get a good fireworks spot. It was a great day. We did just about all the main attractions and were quite happy all day!
The days that are rated at 9 or 10 on the crowd calendars are our usual days in the parks. Just get there at opening, plan FPs (or now FP+ which promises to save me a lot of walking) to be spread throughout the day, do as much as you can before noon and then relax and enjoy the afternoon/evening watching the masses wait 4 hours while you sip on a drink, sitting in the shade, waiting for your next ride!