Legally speaking it's not so much that the taxpayers pay her for existing, as much as they pay her for the right to land that she owns. The queen also funds a significant proportion of parliament. The only way to get rid of the monarchy is to also get rid of private property, otherwise you're taking land that has been given for the public use gratis, and putting it into private hands, since that's who legally owns them.

And if you think we should deal with the monarchy first, and not the big corporations and Russian oligarchs that not only own huge swathes of land, but have contributed significant amounts of funding to the Tory party, then I don't know what to say.