The mistake is that people assume that getting rid of the Monarchy will free up a lot of money that the Monarchy currently receives. Would it? Because France, for example, is a bastion of freedom and wealth redistribution? In fact, its Head of State is doing exactly what our Monarchy is doing (i.e. using, or embezzling, public funds) but in a far more insidious way: at least the Monarchy doesn't pretend it's a democratic institution.
Frankly, the Monarchy is a symbol of the United Kingdom (and not England, as it is so often believed) whether we like it or not. For the UK to renounce the Monarchy would mean renouncing, in a way, its monarchic history, which will not happen for various reasons, be they economic or historic. I think a more pressing concern is the endemic corruption of the House of Lords which does have a manifest ability to affect the day-to-day living of people in the UK. I'd rather people got bent out of shape about that first than however many pence gets paid in tax to our nation's most well-known ambassador(s).