There have been attempts to do what you describe with QoS management,
> where some kinds of traffic gets treated differently than other kinds
> of traffic. In general, these things don't work very well, because
> the underlying protocol isn't designed for it.
No, the "underlying protocol" has nothing to do with it. That's the beauty of IP: it's service-model independent. We have a "best-effort" service now, but a guaranteed service could be implemented without any changes to the IP layer. The reason we don't have one now is the lack of a business model that could support it. (The people I used to work for helped to invent all the necessary technology in the early- to mid-nineties, before the boom created a bandwidth glut. It was a serious research effort back when a T1 was more than most people had.)