The key word in “constitutional monarchy” is “constitutional”, not “monarchy”. The monarch must follow the parliament’s requests, and not doing so is unconstitutional. Parliament is sovereign, at least in all of the countries that derive their monarchy from the UK’s.
Outside of the UK there wouldn’t be a fight anyway: in all the Commonwealth countries (except the ones that have since gone fully republican), the monarch has a representative called “the governor general” who is selected by the Parliament and recommended to the monarch at which point see above. The monarch has to take the advice of who is to be their governor-general. Issues basically never get to the monarch for them to mess anything up. The loyal-to-his-country deputy gets first crack at everything the monarch does in theory and has no reason to go against Parliament. If somehow the g-g or the king did speak out, it’d be a legal mess but everyone would ignore them. Practically we’d either get ourselves a new monarch or just say to hell with it and become a republic.
To answer your specific question then, yes, it’s pro forma. The monarch’s role is to be the embodiment of all legislative, judicial, and executive power, in a fairly close analog to what the American Constitution is. But the Constitution can’t exercise any of those powers and the monarch can’t either. It’s just a historical oddity that they can walk and talk, unlike a piece of paper.
No, they do – it’s just not a codified constitution like almost all other countries have.
Uncodified constitution
Proponents of the idea believe that a constitution that has evolved bit by bit over a long period of time and across a bunch of different charters and unwritten agreements/customs is stronger that one that’s done all in one shot. You’ll see the unflattering metaphor that “a tree is stronger than a weed”, which seems a bit unfair but it’s reasonable point – if not one that’s beyond argument or anything.
Commonwealth countries are politically conservative, small “c” and not big “C”, as the general attitude is “if it ain’t broke don’t fix it, even if it’s objectively kind of stupid”. There was a good reason for every one of the decisions that led to today, don’t &^%$ with it, just in case.