I’m probably one of the more prolific flaggers of common names on here, as the group I work on, corals, has little in the way of a codified common nomenclature. This has led to a variety of competing names appearing in field guides, aquarium literature, and the peer-reviewed literature, along with plenty that have been created de novo on here. To give an extreme example, there are literally thousands of “common names” that could be applied to a genus like Zoanthus using the metric that is being proposed here. There are also plenty of common names that are indiscriminately applied to unrelated corals owing to their superficial similarity. What is a Colt Coral? What is a Broccoli Coral? What is a Brain Coral? It really depends on who you ask. There is no standard usage, so these names are somewhat meaningless.
It’s important to document these names when they are in reasonably common usage, but I’d argue that it’s equally important not to promote a name as being the common name, unless it has a legitimate claim to that title. That’s the problem I see with the default common name as it is used on iNaturalist. I’m not familiar with how the curation of this field works on here, but is it possible to list common names in the profile of a taxon without having any single name show up as the default? I think that would be an acceptable solution to this dilemma of dubious nomenclature.
With regards to the larger point about how we should define common names, I think it’s important to consider the role they are meant to serve. These function as a non-Linnaean alternative to accurately identify taxa. In that sense, it’s vital to properly vet these on iNaturalist, especially given the reach this website has with the general public.
To use a somewhat hyperbolic example… there’s no reason why camels shouldn’t also be known as “lumpy horses”. Here’s a quick Google search showing 3000+ uses of that name for camels. That is, by the loose nomenclatural definition, a perfectly valid common name. I imagine if you ask people what a “lumpy horse” is, a large number could correctly guess a camel. But do we want to recognize that? Is it worth adding “lumpy horse” to the list of acceptable common names? This is why I strongly advocate for a standard of some sort being used for these names, something more robust than “it’s a name that appears on the internet somewhere”. Peer-reviewed journals, published field guides, and official lists from biological organizations are the gold standard for what constitutes a good common name, the sort that can safely be used as the default common name for a taxon on here.