Well, I'm gonna go against the grain here and say that it isn't rude to save these seats or chairs. It's the way it's done in TV...for whatever reason, it has been accepted behavior for years. Personally, I don't engage in the practice of saving seats, but I have friends and neighbors who do. However, they stay with their reserved seats/tables all day.
What can the event staff do? Here's a tip...
Yesterday, I was at LSL, where my some of my neighbors had been saving a table and chairs since 5:00am. When I was there, the sun was starting to hit their spot and it was getting very hot. One of them owns a fold-up tent, like they use in the squares for market night. I asked him why he didn't just throw up the tent until parade time to get out of the sun. They told me the "staff" does not allow you to have any umbrella's or tents. They laughed at my suggestion, as if I'd just hopped off the turnip truck..

So, there is some control exercised by the staff.
OK...here's the best part. I texted my friend about 6:00pm and asked him how the celebration was going at the square. He texted back, "We're at Cane, waiting for a table. If you've seen one parade, you've seen 'em all."
You gotta love it . . .