Let us not forget the diplomatic aspect they afford and I'd say from that aspect alone - done more good than the elected politicians. Whilst the media love to focus upon the negatives, you can't overlook the positives and initiatives - the prices trust and other chartable involvements and then tourism. Though the diplomacy aspect is something that you have to respect the Queen and been a national asset in that respect.

So far from a no-brainier as you say if you look at their involvements beyond the headlines.

As an aside - if America had a royal family, the prospect of Trump on legal currency bank notes would be zero.