That doesn't seem to address the natural follow-up: what stops me from claiming all my traffic is VoIP so it gets processed faster? Is there some offsetting downside that disincentivizes someone from labeling it that way? (something like "any request for lower latency will also reduce your throughput, so don't call it VoIP if you really care about the overall transfer rate)

It's fairly straightforward: everyone gets high priority up to X mbits/s with no upstream oversubscription. Everyone gets best effort up to their last mile speed after that. If there's still available bandwidth, everyone gets idle-only traffic without a cap.

You could add more priorities in between, etc. as needed.

Then that just means everyone will call their first X mbit/s "high priority" and then relative priorities are unaffected and nothing can be privileged.

That makes no sense. The first X mbit/s will be privileged. If you waste your priority allotment on torrents instead of voip that's your choice, and that choice doesn't affect anybody else.