Like the enlightenment and the industrial revolution, democracy wasn't imposed, it came into being here for the first time, and while it's not perfect, there's a lot of factors, including sentimentality and inertia, keeping the status quo going. You could argue that a clean start with a proper written constitution and federal government (with separate state governments for the different countries) would be a good move. But like for any working system, it's painful to disturb entrenched structures, and there's always the risk of breaking something important. The US was able to do a better job; it's easier when you can start from a clean slate with the knowledge of hindsight.
Also, the monarchy has for the most part been a net positive. Compared with what elected MPs have done to the country, I see it as a rather more benign institution in comparison, in recent centuries anyway.
I know I'll get downvoted, but I am genuinely amazed by how a small minority of people can gain so much control, and absolutely no one complains. I know there are historical reasons, but it is fascinating nevertheless.
But now, you have a problem in that your Parliament is essentially unchecked, and e.g. all your human rights protections are mere laws that are within Parliament's authority to repeal (well, and ECHR, for now - but even there UK got a special exemption for this exact reason).
You know that the Queen is still the head of state for most of the commonwealth countries? And half of Europe still have Kings and Queens, and quite a few countries in Asia. I wouldn't be surprised if over half the nations of the world still had a monarch.
Plus it didn't happen in 2019, it evolved over more than a 1000 years. Things get a little warty over that period of time.
The Commonwealth has 53 member states, only 16 of which have the Queen as the head of state. And those 16 contain only 6% of the Commonwealth's population (144 million out of 2.4 billion).
List here for everyone else https://en.m.wikipedia.org/wiki/Commonwealth_realm
If you make a new constitution under the current system, it can always be undone-they _can't_ abandon that power. Furthermore, Parliament doesn't have the power to get rid of the Queen, but Parliament requires the Queen in order to have power so she can't remove herself. If you change it on a standalone basis, and completely abandon the old ways, what legal authority do they have to do that, and will it be recognised? I imagine the Courts especially would be sceptical about such a big divergence from the constitution (without an intervening event, which seems unlikely given the Queen polls well).
Realistically, the Queen only have has power on paper (she can never exercise it, except as required theoretically to give power to democratic decisions), so it'd be a big upheaval for little gain.
In theory. In practice they can, and have.
What proportion of people in your country support your head of state? I guess it's less than 75%. Ours really represents most of us.
The effective head of state is the PM.