Which is fully appropriate where it exists.
I would be 100% against the US having a 'Constitutional Monarch' but I'm 100% in support of the UK Constitutional Monarchy, given that it has come from their long established culture, nearly a 1000-year-old 'contiguous-ish' institution.
FYI in 1258 the Monarch signed documents which required him to 'Confer with Parliament' when changing rates of taxation. That's only 40 years past Magna Carta, and the first reference to 'Parliament'.
The romantic in me likes to believe the Queen would step in if the British parliament tried passing some truly terrible bill. Basically acting as a last stop gap of human and British sensibility. Though with Queen Elizabeth II gone I'd have less trust in the judgement of a monarch.
Part of me does wonder if US politics would've been much different with a ceremonial figurehead. And that'd be a fun alt-history where a great-great-grandchild of George Washington is the ceremonial head of the US government and has to deal with intrigues of Washington politics while just wanting to live quietly on the ancestral Virginian home.
The reality is that it’s consistently been the House of Lords that save us from the nuttier ideas.
You have to remember how old she was. The Queen's first Prime Minister was Winston Churchill, born in the 1870s. A staunch Empire man to the last, he was one of only two Prime Ministers for whom the Queen attended their funeral. He is famous for successfully defeating Europe when it was united under a dictator determined to reduce Britain to rubble and ship its population to labour camps. She was Queen as the British Empire wound itself up and became the Commonwealth. She saw the nationalization of the British railways and then the re-privatization of them decades later. She saw the birth of the European Coal and Steel Community, she watched as it evolved into the European Economic Community, and then into the European Union. She saw Stalin fall, then she saw the Berlin wall fall, and then the USSR. She observed passively as millions of people from the former Eastern Bloc then moved to the UK a decade later to make a new life. She saw the atomic bombing of Hiroshima and Nagasaki. She saw the space race. She was Queen throughout the Troubles, living with the constant threat of being assassinated by the IRA, who at one point dropped a concrete breeze block on her car. She visited over 100 countries. She watched as countries fell to communist revolutions. She watched her country be brought to the brink during the Winter of Discontent, she watched as European nations transitioned from dictatorship to democracy. She watched global COVID lockdowns. She watched the Euro debt crisis and a thousand other crises come and go.
In short, she saw political institutions far larger and more important than British membership of the EU rise and fall over her lifetime, and far more dramatically. She saw the UK join the EEC, she saw it transform into the EU and then she saw the UK leave it again. Of all the things she's seen and done, of all the life and death battles she witnessed or even took part in, EU related events were surely some of the less memorable and important, especially given the relatively imperceptible changes Brexit so far brought about.
If you really want to engage in speculation about the Queen's views on Brexit and the EU, consider this. I already said Churchill was one of only two Prime Ministers the Queen honored by attending their funeral. The other was Margaret Thatcher. Both had complex views on the merits of European integration, with both being positive in their earlier years but coming to regard it as a mistake in their later years.[1][2] Both were strongly committed throughout their lives to the strength and independence of the United Kingdom regardless of what Europe did.