It works in the UK. Italy changes leadership often, and a monarch could provide at least some symbolic unity and stability. In Thailand, which has become volatile in its government, at least has the King for unity. Sure, Italy is not the same thing, but having a symbolic monarch as many European nations do shouldn't be too problematic.
Dude, if you really want to defend constitutional monarchy, Thailand is probably one of the worst examples you could possibly come with... Well, unless you're an Opeboist. 
And anyway, if you look at the way Italian monarchy provided "stability" in the past, I wouldn't exactly consider it a good thing.
Counterpoint: Juan Carlos of Spain.
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