A public right of way is just what it says. People have a right to use it, for whatever purpose they choose.
Most of the congestion is in the National Parks. Race organisations already need permission from the National Park authority in order to run them. So no banning by landowners is required. All that would need to happen would be the NP to give out less permissions.
They already do limit it in AFAIK quoting "damage to the fragile environment" which is a valid concern. The argument is what that limit should be.
I'm guessing most people wouldn't want an organised event on every peak, every trail, every beauty spot every single weekend. Therefore I'd say that all of us do have a limit. The point of contention is what that limit is. For me, I think it's getting too much now in some areas. Others are free to disagree.