My suggestion: edit the page, explain at the top of the page (before the table of contents) how to get an up-to-date list using taginfo.
Other than that, maybe follow the deletion procedure anyway, at least to get an admin's attention. This page really doesn't make any sense if it needs to be updated manually (even if it's with a script) when automatically updated info is available elsewhere.
Note, I have extremely little experience with the wiki, this is just my interpretation of the situation.
@redd maybe better update it and do not delete it because all the common Mapping Tools like iD or JOSM still only refer to the wiki, not to https://taginfo.openstreetmap.org/ ?