This is exactly what the article is about.
This is the system of government that the people of Britain have chosen, and the impact of the queen is exclusively a political problem. If there was a serious difference between the will of Parliament (Commons) and the Queen, the result is a foregone conclusion.
There is surprisingly little basis for arguing that the people of the UK have ever chosen almost anything important about our current system of government. That system is largely based on historical conventions, often dating back centuries and in some cases to the outcomes of civil war, and the status quo has several built-in feedback loops that make it difficult to change even with widespread popular support. The constitution of the UK is a fascinating subject, but it can also be rather uncomfortable subject matter to study if you believe in ideas like democracy and civil liberties.
As a "person of Britain", I have certainly never had any say in the system of government.
The article is actually making a big deal about the fact that the queen expressed an opinion about legislation in an area that the author decided wasn't covered by the vague wording of a pamphlet.