The monarchy provides much more stability to the UK than many realize. The UK has been transformed from a British Empire composiong 25 percent of the world's people to a nation that is fifth in enconmic power. The monarchy helped keep things stable during that time. Problem is Elizabeth is 77. I remember her being the modern monarch when in elementary school. She broke barriers and was hailed as the Queen who brought the monarchy into the 20th century.
It is doubtful that at age 77 she is going to make a lot of more changes though she did changee the succession to the oldest child, not the oldest son. The Queen was the third longest reigning monarch in English history some 15 years ago. I thing she has moved into second place now. Victoria reigned longer. Elizabeth I also had a very long reign.
Most of the cost of maintaining the monarchy will be there. Windsor Caslte and all the other Palaces and Castles must still be maintained. The Queen is wealthy and a lot of her expenses she bears personally. All countries with a parliament system have a head of state and a prime minister. So a "President" would still have a salary. So there is money to be lost from tourism and no gain in government spending if the monarchy is abolished.
I suspect the Elizabeth's popularity will grow as she gets older. Her mother was extremely popular. Charles is already doing most of the international "state" visits. Elizabeth has not attended a state funeral for 10 years sending Charles to represent her. We will see this more and more. An aging lady appearing on the balcony of Bunkingham Palce waving while Charles reads the speaches. While Elizabeth will likely live 20 more years, PHilip won't. In my opinion, Philip has been the architect of much of the monarchy problems. He was overbearing on Charles, cheated on Elizabeth, and in general is not a loving man who wins the approval of the people. When he dies, Elizabeth is likely to become more open and friendly with the people. Elizabeth has let Philip have way too much say in royal affairs.
Just an American talking here.