Yes I would disagree with your framing of you hypothetical not least because parliament did kill the king (Charles I), then once the lord protectorate was over

Yes I would disagree with your framing of you hypothetical not least because parliament did kill the king (Charles I), then once the lord protectorate was over and the restoration conspired successfully with a foreign king to over throw the current king and then wrote a document deciding who can and can not be king which has applied to all king and queens so far. Parliament wants the king as a figure head so they can hide behind something, formally it's not Parliaments government by it's self but the monarchs, though the monarch may not raise an army or really have any power outside parliament but still the monarchs government and should things go badly they may simply blame the figure head. Once you see the pattern you will see it lots of time's in are history maybe other histories ;) .