Turning back to the problem statement in your proposal:
This solves the issue of multiple images representing the same OSM element, such as when a large feature (such as a mountain) has many angles that may want to be captured. Currently, this relies on a contributor or data consumer to create and link to a single category in Commons, which may not show the entire picture (such as “[Mountain] from [Nation]” categories where multiple would be valid and useful)
A “Category:Mountains in country” represents a broader concept than a particular mappable feature. The wikimedia_commons=* tag needs to be more specific: “Category:Mountain Name”. If such a category doesn’t exist, you can create it or omit the wikimedia_commons=* tag.
Personally, I very rarely tag wikimedia_commons=* in the first place. Instead, I set the feature’s wikidata=* tag to the QID of a Wikidata item representing the feature, then set that item’s image (P18) property to the name of the file on Commons. Wikidata also has a variety of other properties that link to Commons, such as Commons category (P373) and Commons gallery (P935) for when no one image is unquestionably the feature’s most representative image.
If Wikidata doesn’t have an item about the feature yet, you can add one. Under Wikidata’s very lax notability rules, the item is guaranteed to be notable because it has one of these statements linking to Commons. For many classes of concepts, such as buildings, hotels, hiking trails, monuments, and campsites in Sweden, the Wikidata community has created a tagging schema that enables you to create the item easily by filling out a simple form.
When would I use wikimedia_commons=* alone? When the feature is so obscure that I’d feel really silly for making a dedicated item about it, like an ordinary trash can on the sidewalk or this quirky traffic sign that has a single usable image and nothing more to say about it.
Commons isn’t quite comparable to other image hosting sites or the image=* key, because it’s part of a system of Wikimedia projects that uses the QID as a persistent identifier, as the single entry point to Wikimedia from an external database such as ours. We mappers can easily verify that the QID is correct by viewing the wikidata=* tag on the main OSM website. And for OsmAnd users and probably others, this is just an implementation detail: they just see the photo or photo gallery.