That’s certainly an interesting use of the network tag, and one that would need amendment to the linked wiki page if adopted. I do think it’s redundant to add both a base tag with free-form text and the :wikidata variant of the tag. I understand adding it for existing tagging (e.g. having both operator and operator:wikidata because operator has existed for a long time as a tag). I’m really not a fan of proliferating of that pattern for yet another base tag, and it risks the two tags getting out of sync.
If the goal of the base tag is readability on osm.org, I do remind folks that there’s a browser plugin that will do this for you:
Agreed, we spent quite a long time thinking about park and protected area tagging, but the current guidance is more “a couple guys thinking really hard and deep about the problem” than “wide community consensus”. But so far it seems to have stuck.
If I’m reading the tea leaves correctly, I’m guessing there is probably a desire to have sufficient tagging to distinguish different categories of public lands for rendering. I would agree with what @ezekielf hinted at, where the operator:wikidata/protection_title combinations (or the straight operator tag if you must) provides sufficient information at render time to make that distinction.