The built-in templates and their tags are really nice,

but I find the number of built-in tags to be overwhelming.

For example, when I tried to apply my new tag, the always-present tag noise makes it very hard to see which hosts are already tagged and which ones were forgotten.

I know I can search for VMs missing my new tag, but then I have to open another search to see what is the tag value on the related hosts.

I see two possible ways to go. One would be "hide factory tags by default / unless explicitely mentioned in tag display priority". Other would be "strict mode for tag display priority", where, I don't know, you can end "tag display priority" by a dot to say no other tag should show.