Ummm, I fail to follow? That is exactly the reason why using name:xx would work greatly.
As this is OSM: British one, of course 
More seriously: yes, I am simplifying, in order to get coarse point across first. If the need for that level of precision becomes high, there are already standards to do that: one could use en_US or en_GB, etc. But even without that, I’ll bet you that average British citizen will prefer to handle the name in en_US and Latin script instead of KP name in Hangul any day of the week.
Another point: I’d wager that it is not British citizens that are outraged and ready to go to war because USA is starting to call it Arabic gulf instead of Persian gulf. More likely, it is countries bordering that gulf that are getting most agitated about the naming.
I absolutely agree with you. Which is why my “proposal” didn’t say “Display name:en always on osm.org”, but instead “Display user-prefered name:xx on osm.org” (i.e. the one at Preferred languages section at https://www.openstreetmap.org/preferences if you’re logged in, or one that your web browser sends if you aren’t)
do you more like a shameful to you, but readable to others ‘name’ for a place in Croatia?
I’d prefer that everyone would call Croatia with its proper name Hrvatska with correct pronunciation (and that everyone speaks Croatian while we’re at that - I find using foreign languages like English somewhat taxing), yes. But I also understand that that is unreasonable demand of others.
Thus, the proposition: Those who like the name “Hrvatska” should see that, those who prefer “Croatia” see that, and those who prefer “Хрватска” see that, etc.
Problem: there is no local language for international territories.
No there isn’t (or we’d just use the name tag in that language, obviously!), but there is a local language that the user of the OSM map is speaking. And they always know what is the language they want to see. For me, that is Croatian. Even if I am looking at the map of North Korea, or the map of the Mexico, I want to see their names in Croatian. That is what I am suggesting. Show each user what they personally want to see.
Watching the Atlantic Ocean: repeated name removal debate the osm community has not found a solution for this yet.
They have, see e.g. this map here (and change the language to the one that you prefer, obviously). It is just that the map displayed on osm.org haven’t caught up with 2020s yet. Hopefully they will soon.
- for politically disputed areas we could also more strictly use A/B names with unpolitical ordering like A being the name that existed first or the first in the alphabet
Sounds like fun; let’s start with renaming North American cities with Algonquian names! Never did particularly like that “New York” name anyway, surely nobody else will mind either, right? (hey, it comes first both historically and alphabetically) 
