Maybe because the Monarchy is the oldest Monarchy in the world going back thousands of years? If so, then it fits my theory of never fix that which is not broken.

GOOD QUESTION!
TRADITION, is part of most British people.
TOURISM, much money is earned by tourists who would not come here without a Monarchy to look at.
A LOT, of European countries still have a monarchy, maybe not so famous as Queen Elizabeth, but still Royalty.
WHY NOT, Typically British. "Querky".
*****
I see both sides. I am 63 years old. Lived in a Republic for 20 years. Wife is African. I am open minded.
Thanks for your interest in my little country!!
Best Regards,
Adrian Jarvis.

The British have always chosen the quirks of our history against foreign rationalism. The Romans brought us straight roads and decimalisation. As soon as they left, we reverted to impossibly complicated Imperial measures and winding country lanes.

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In trying to explain the unlikely success of the monarchy, we shouldn't expect the answer to be based on reason ”

The Normans commissioned the Domesday Book to try and impose order on bureaucratic chaos but had to compromise at every turn. That is how we ended up with something called Worcestershire - a place that foreigners find impossible to pronounce, never mind spell.

The British don't like straight lines. When we look at those maps of the United States with ruler-straight state boundaries, we feel pity. Walter Bagehot understood that our identity is found in the twists and turns of a rural B-road, not in the pragmatism of a highway.