If it wasn't Sophie (who is pretty in offensive) it would be an extra layer of politicians who at least half the population at any given time would be infuriated by.
I don't why people don't think this through.
Most western dmeocracies have a double layer of leadership - president/ prime minister (like France) or president / chancellor (Germany) , or monarch / prime minister (like us and the Nordic countries). One is usually head of state and the other head of the executive (the bit with the day to day power).
So if we were not paying for Sophie we'd be paying for a president's security. and unlike Sophie who has been doing the job since 1998 and will continue for the rest of her life elected officers change every 4, 8, 10 years and in most countries they get protection for life (and often for their families too, who might do nothing for the country at all).
So we could be paying for the security for 5 or 6 or more still living ex presidents, spouses and families. Instead of which we have non-political people in our royals who we pay for because they are giving their lives to service (you can be smug and silly about eating cake but you must know that's a pathetic attempt to summarise what they do) and most of them keep going decades past the retirement age. The Duke of Kent carried out 78 engagements last year and Princess Alexandra 44 despite both being very frail and in their late 80s.
with hevery decade there are fewer working royals being protected not more. The oppostite would happen is we were a republic.
Far from being expensive, they are very cost efficient. This is not in itself an argument against a republic - you might believe a republic is worth paying for but make that argument including where the money would come from instead of bleating about royal security costs without thinking it through.