I'm not at all a traditionalist per se, but I do see advantages in a non-political head of state.
Let's take a concrete example' the Weimar Republic. Due to the Great Depression combined with the Treaty of Versaie, the Germans were humiliated, out of work, poor, you name it. So they started to turn to extremist parties, both right and left. Unfortunately, with a democratically elected president, it was easy to dispose of him based simply on "the will of the people". After all, they'd voted the Nazis in for crying out loud! How much more democratic can you get than that? Now had the president not been elected but rather held a position of sovereign above and beyond the will of the people, he could have possibly had the power to prevent the Nazis from taking power. After all, don't forget that the Nazis had been voted into minority government pocition a few times, each election giving it more desperate votes. Yet because the president was elected himself, his intervention could have been viewed as unappreciated by the people who'd voted for the Nazis. An appointed soverign however, wouldn't worry about that 'cause he's beyond the reach of the people anyway.
In Canada likewise, we had a rise in both fascism and communism in teh 30's. The UK witnessed the same thing. But the UK was saved by the conservatives and Labour party who could take votes away from teh two extremes. Canada likewise with the CCF and Conservatives. But let's say there was no conservative party at that time. Then the fascists could potentially have taken Canada. Or if there was no CCF, the communists could have. If the executive is elected, then the extremists could have taken that position too, but with a king or queen, he/she could have easily refused to dissolve a minority parliament due to the turmoil of the time. This applies to both the UK and Canada.
Now let's say the same thing should have happenned in the US. The president himself would have been vulnerable to the whims of a desperate populace of the time. And who's to say the economic crisis of the 30's couldn't meet a parallel in the future, with Islamophobia, or some other boogie man taking over just like anti-semitism and such in the 30's?
I say keep the monarchy, even if I'm not a traditionalist.