Having looked at the fees of the event you linked to, that's in line with what a cycletouring club will charge ... in other words ... cheap.
You say ... "Do that many people really pay so much to do something that is essentially free?"
But cycletouring is NOT free. The $120 registration fee includes Overnight camping (Saturday to Thursday), and a whole list of other things. That's 6 nights of camping for $120, or $20/night. That's pretty reasonable ... it's the amount you'd be paying for a campground site if you were travelling on your own. And $6 for breakfast and $10 for dinner isn't bad. You've got to eat when you're cycletouring, and one of the nice things about an organised tour is that they provide the food for you right there where you end the ride. You don't have to go looking for it.
Granted you'll have to pay more than that because you've got a family, but if your kids are under 17, the registration fee is half price.
Go look up Exodus tours or Backroads Bicycle tours for an idea of how much they charge.