True... she’s a figure head. I don’t know how bad things would need to get before she would refuse to be a figure head for them. It’s just weird.
She’s not only the Queen of England (or Great Britain even) — she’s the Queen of all 16 nations in the Commonwealth Realm (that includes Canada, and Australia). She, or her representatives (various Governors General or Lieutenant Governors General) give assent to all legislation passed by every nation, province, or territory in the Realm.
If she were to refuse assent on a Bill that had wide popular support (usually gaged by the fact that it was duly passed in Parliament), it would likely mean the end of her reign — at least within the particular dominion, whose legislation was affected.
The constitutions (both written and unwritten) of the Commonwealth Countries have evolved to be quite different from that of the USA. (For that matter, even your written constitution has evolved substantially over the years.) The reigning Monarch simply does not have near the powers of the “ruling” U.S. President. The U.S. President is both Head of State, and Head of Government; while the Queen is just Head of State, and various Prime Ministers are Heads of their respective Governments.
Americans fought a Revolution (in part) against the British Monarch of the day — it’s a bit ironic to see Americans on this forum demanding that the current Monarch be more dictatorial.