Realms vary widely as to their types of governance, and the label "monarchy" or "republic" means very little nowadays. The best (or worst, depending on the point of view)-case example if probably D'Hara. I don't think I have it in me to summarize D'Hara in a forum post right now, but in case you're interested you know where to look.
Suffice to say that your assertion that "there are no parliaments in BM" is demonstrably false.
I stand corrected. King Chénier and Queen Elizabeth are kindred spirits. The type of government should definitely be factored into the equation.