That's the essential genius of constitutional monarchy - by investing the royal family with immense status but no actual power, we reduce the status of those who wield real power to mere public servants. The Prime Minister must ask the monarch's permission to form a government, in the knowledge that the monarch has no actual power to refuse. Those who hold public office swear an oath of loyalty to the monarch, in the knowledge that the monarch's power is wholly and irrevocably delegated to parliament and the judiciary.

The monarch is in essence an empty vessel, symbolising whatever version of Britishness we happen to believe in. Regardless of the government of the day or the divisions that may arise in society, the crown endures. The man or woman responsible for running the country does so as a temporary custodian.

Britain is dysfunctional in all sorts of ways, but the parts that function best are extremely Lindy. The monarchy, like our unelected upper house, is completely idiotic in theory but incredibly successful in practice.

The royals wield immense soft power, plus all of the power they have by virtue of the country's constitution.

It's still a governmental role, and a political one, and anti-democratic.

But is what you describe a good thing? People seek status. By removing status from being Prime Minister you make being Prime Minister merely another step on the path to status. I'm not sure it's a good thing for someone to see being Prime Minister as a means of leverage to something else they want.

UK is a weird outlier, because the royals aren't really leaders. Their role is almost clerical, rather.

Had thought recently their role is to squat on space that a would be fearless leader would try to exploit.

The UK deal with the royals is really quite different. There may be an over-fascination but there isn't a huge amount of deference, and if the royals want to make things happen that are not popular, they have to use very twisty back door routes. The (public) relationship that even fervent royal supporters have towards the royals is nothing like the (public ) relationship with Stalin et al.

Also, it's pretty easy in the UK to say that the royal family is stupid and they suck and they leech money from working people and nothing will happen.