The argument is based around the millennia old tradition of having a leader. The queen of England is a world known figure. As a statue, but not a powerful entity. The idea of parliament has gained popularity over the past 900 years(in England) and has turned England into a constitutional monarchy. The queen is the boss! Not the PM. The queen should step in when there are situations in which the government has overlooked something. The queen has no function at the moment. If this great and biblical idea should be kept as an example of good government and economy, then why not keep the retro trend in fashion!
I would like to accept this topic. You argue we should give the Queen power, if we're keeping the position of the queen. The reason why we got rid of queens and kings is because if they had power, they had absolute power. With the power to do anything with your society can easily lead to abuse. Your proposal of the queen fill in positions where the government over looks is in contrary with what the roles are suppose to be in a monarchy. It makes no sense, and what positions would the government have overlook that the Queen needs to fulfill? If there is anything critical than there would be an elected office. The Queen isn't suppose to function. She's a reminder of the UK's history, and is essential a celebrity. Also the Queen with her infulence can do many things without directly doing anything like you're suggesting.