In 7+ centuries Britain(/UK) the ruling class never had a revolution/civil war that lasted longer than a generation, hence the builtin default action is to continue with the monarchy and associated class system. This also avoids all the (enormous) internal and external turmoil I cited. (PS In the age of social media I don't think you can call a popular referendum 'democracy', Brexit being the very obvious example. It depends on how literate the electorate at large are, and how tight(/loose/nonexistent) the controls on media spending to manipulate them are.)
Whereas in Japan, it was the US occupation post-WWII which intentionally decided to keep the monarchy for social cohesion, while reducing it to being titular, and abolishing the nobility. This was the US's (and MacArthur's) architecting, not Japan's. It's not like Japan had a referendum or parliamentary debate about the Showa Consitution [0]. And one intent was to prevent Japan fracturing internally, but to keep it from going imperialist again, and totally dependent on the US militarily. (Japan didn't even have provision for a constitutional referendum until a decade ago, and if it ever achieves the 2/3 support to have one, it'll more likely be about removing the Self-Defense Clause than abolishing/reducing the monarchy.)
It would be an interesting what-if to conjecture how the US might have reshaped Britain in the 1940s, like Japan.
Re your article, it's a strength not a weakness that the US doesn't have a national/federal referendum, most states have a pretty active ballot initiative system, so e.g. state taxation, legalizing marijuana etc. can be tried out and then we have statistics to inform federal (legislative) policy-making, plus there's less inertia to undoing bad decisions, like when Michigan nearly taxed itself out of existence and all its jobs and young people emigrated (internally).
I wouldn't say the UK has a disciplined approach to referendums. You can't even tell what % of GDP was spent (by third-parties) on political/social-media influence campaigns during 2015/6 (Brexit referendum), not even now a decade later. Not just [1] but all the other campaigns and interest groups.
[0]: Showa Constitution of 1946, seems pretty clear it was authored by the US not Japan [https://en.wikipedia.org/wiki/Constitution_of_Japan]
[1]: "Arron Banks and the mystery Brexit campaign funds", FT 11/2018 https://news.ycombinator.com/item?id=18382116
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