I'll put it to you this way. Firstly, anyone can become a monarchist. Therefore, the monarch can agree with any political party. Secondly, the monarch can be backed by a political party, but the monarch does not have back that party. Thirdly, if the anti-monarchists gain enough power, the monarch cannot stop them.

In other words, I believe that a monarch is much more non-partisan than a President. A President can support the goals of his party. A monarch can support social democratic goals at the same time as supporting conservative goals - and because he has no electorate to appeal to, they won't vote him out for betraying the party or his idealogy, because he simply doesn't have one (at least not in public).

I believe monarch's tend to be less partisan than politicians, but by creating a means by which a monarch can be removed you created the need for the monarch to play to public opinion, which in my mind removes the best thing about a monarchy.

I think instead of a monarchy maybe a council of intelligent people would be a better tool, you could have leaders n business the sciences ect. they could serve something like a 5 or 10 year term and after that they are simply replaced, unfortunatly then you get down to specifics of who picks the candidiates and it would have to be members of parliement, and in the end party loyaltys would take over and it would turn into a glorified extension of parliment..