We'd need an Internet Protocol that would support the opposite of net-neutrality. Basically, only allowing important traffic and blocking or downgrading everything else.

That was part of the original ip specification, it was modeled after army telecom patterns. where there are priority levels baked in. when the net starts to overload the lower priority traffic gets discarded first.

https://www.rfc-editor.org/rfc/rfc791 calls it precedence

  Precedence

          111 - Network Control
          110 - Internetwork Control
          101 - CRITIC/ECP
          100 - Flash Override
          011 - Flash
          010 - Immediate
          001 - Priority
          000 - Routine

The bits ended up being reassigned for service codes. mainly because nobody used them. I also suspect there would be problems with a priority system in a peer network like the internet. It works in a more managed network(like the army) where strict priority control can be enforced. but it would probably be an arms race when one peer starts setting their priority a notch higher so their messages start getting through better on a congested link.