Do you want air traffic control to be on the general internet?

That seems like an extremely foolhardy thing to do.

As a tertiary backup: Yeah, maybe I do want that.

It seems like it would present a less-chaotic solution than that provided by having no data communications at all.

You certainly don’t need to run this over public Internet to get resiliency over multiple paths.

Why not? Assuming it's competently set up - serious encryption, details not blabbered about (to attracted DDoS or whatever), etc.