Jo

I basically take the Clement Attlee stance. We're always going to have patriotic zealots pouring nationalistic hero-worship at the head of state. If we're lucky, said head of state will be some totally powerless figurehead who can't combine that hero-worship with actual power to start wars. If we're unlucky, said head of state will have significant legal powers, and will combine populist kowtowing with their formal governmental prerogatives in order to invade Canada or exterminate undesirables or what have you. Right now, a significant portion of Tory ride-or-die loyalty is directed at a man who has no actual power whatsoever; can you imagine if all of that was redirected at Rishi Sunak? 

I'm not saying that monarchy is always a good thing. But it is one way to avoid George W Bush. 

(There is a balancing act. We want the monarch to be sufficiently legitimate-appearing that he actually gets the hero-worship. But we also want him to be so blatantly illegitimate that he doesn't dare step a foot out of line lest he be introduced to le louison. The British are gradually realising that monarchs are just corrupt randos, which is unfortunate for this balancing act. Perhaps we should take the Irish/German route and elect our powerless figurehead. Or we could have some sort of elaborate selection process  –  that would be fun to design.)

Another benefit: they're great for building unity! Because Lizzie 2 was an apolitical sweet old lady (mild racism notwithstanding), everyone could get behind her. We pay these idiots less than the Red Sox, and in exchange they give us decades of photo ops, handshaking, and senile smiles  –  that actually work. Even if we'd squeeze just as much money from tourists after guillotining the royal family and expropriating the Sovereign properties, we get half our national unity for less than the cost of a baseball team. As patriotism-building exercises go, the Mountbatten-Windsors are an incredible bargain. 

Also, don't Americans love parades? Yes we do.