Looks like defining “what a path is” is not a viable option.

I think that a lot of issues would be solved by agreeing on
a. Acceptance of the range of real-world features tagged as highway=path (and describing this as fact-of-life);
b. Establishing a set of tags that adequately describe specific cases or country-specific rules
c. Establishing a world-wide set of implicit and default tags;

This would be the anchor for mapping, validation, QA, rendering and routing, regardless of which tags are chosen. It would be a compromise, so everybody will be unhappy about some aspects, but also everybody should be happy about other aspects.

I think a. and b. are not that problematic. Current practice is well underway.

c. is a subset of b.
Establishing this would require mappers and mapper (sub)communities to look beyond “what is a path in my neighbourhood/region/country” to “what is a viable world wide default”.

Example, not for path but for cycleway: in Nederland a cycleway along a road is by default oneway, but the world wide default is two-way cycle traffic. So we explicitly tag oneway=yes on all oneway cycleways along roads, AND oneway=no on all two-way cycleways along roads. That’s a bore, but we mostly use presets for this, and that is the thing to do once world wide tags and defaults have been established.