Cromwell was an aberration. Besides, he was king in all but name. But Lord Protector could easily have turned into a hereditary title if Cromwell's son hadn't been such a dolt.
The shogunate kind of make's Red's point. During that period the emperor was a figurehead, the real power was in the hands of the shoguns. Yet the imperial throne was retained. That's where Britain is today -- a figurehead monarch with no political power, which instead lies in the hands of a professional bureaucratic class (shoguns, parliamentarians, etc.). I can see the parallel.
The shogunate period is not exactly brief. It's nearly seven hundred years. When the emperors were restored to power, less than a century later, they were forcibly removed and stripped of their sovereignty.
I'd be fine with having a Queen that wasn't a sovereign. That'd be good.
Anyway, if it works for them, what do you care? Whatever your view of how she got there, the Queen is not some ravening madwoman reigning over an enslaved, oppressed people. Some of the most progressive, egalitarian countries on Earth also happen to be monarchies. I'm thinking of countries like Sweden, Norway, Denmark, the Netherlands, Belgium, Luxembourg, etc. See? Royal trappings for me, hippy-dippy liberalism for you, pot for both of us, it's all good. Who says you can't have it all? 
You included Denmark in the list. Do we have to have this discussion again?
See, I used to live in Iceland.
Icelanders have a saying. Well they don't really. But it does appear in one of their prominent historical works. That saying is, "Iceland is a land free from kings and other bandits."
Iceland's the only Nordic republic. Part of the reason why it's better.
