The discussion was initiated several hundreds years ago and is still going. Approximately 80% of the population are in favour of keeping the monarchy in its current form.
They also have lobbying and political power, at least in the UK.
Also, it's not the living monarchs that attract tourists. It's the buildings, the places, and the history. Just look at France and Versailles. You do know what they did to their monarchy, right? It's the place and the history, that people go for.