The preservation of traditional institutions (like monarchy) does not have a direct influence on HDI. Both high HDI scores and the fact that traditional institutions (no matter how expensive) are preserved has to do with long sustained periods of political stability, physical security and as a result, economic prosperity.
I think monarchy is irrelevant for HDI and the correlation is more about long term political stability rather than better politics. My country (Finland) could have been a monarchy but ended up not being so. I can’t imagine what could be better with a monarch.
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.
None of them are constitutional monarchies in quite the same way the UK is? The UK has a uniquely intact monarchic system.. But then, the UK is an outlier in many things when compared with similarly wealthy countries.