Royal funding: a proposal

Yesterday we discovered that the taxpayer footed a £40 million quid bill for the Royal Family last year, minus security costs. Some people are worked up about this. £40 million quid is a lot of money, paying a hereditary elite family a salary every year appears bizarre, and having a Monarchy at all is anachronistic. I am nominally a republican, but do not feel it is an important issue now, there are better things to be worried about, and I am rather pleased it isn't really on the political stage. I feel a fair solution to funding of the Royals would be for £1 to come from each income taxpayer which can be opted out of, or indeed increased if the person so chooses. This way the Royals get the funding that the people are willing to accord them.

Is there a gaping whole in this logic?