If we agree to measure political stability as world bank does, the only countries more politically stable in the world than Finland in 2015 were Switzerland and New Zealand.
I fail to see how making Finland more stable would improve anything, or that adding a monarch would achieve this goal.
Royalism sounds like the hunt for a silver bullet that would fix complex problems and institutions in a society. I don't think there is any evidence quasi-religion by itself improves institutions.
There’s no discernible difference on this count between Finland and its Nordic peers that are constitutional monarchies.