The wiki is descriptive, not prescriptive. It should document actual usage which often differs from proposals, especially very old ones.
I’m not sure if you are aware of the recent very extensive discussions about highway=path here on the forum, but these points have come up and have been answered multiple times and I’d rather not re-hash the entire discussion here.
TLDR:
It’s ridiculous and actively endangering people and causing rescue operations that these two kinds of ways are using the same tag in OSM.
highway=footway/cycleway/bridleway/path are about more than just legal access and have implications about the quality of the path and the practicality of using it. Sub-tags can mitigate some of this but are inadequate for solving this issue.
As a sidenote, I’m curious why people keep insisting that footway/cycleway is only about legal access when that is completely untrue for other highway=* tags.