As you well know, the country makes a tidy net profit from the royal family. That's guaranteed because the money paid to the royal family (most of which goes on expenses that would still occur in a republic anyway) is 15% of the 100% supertax the Queen pays on a big chunk of her income. If you give me £100 and I give you £15 of it back, are you sponging off me?
Or are you advocating that inheritance be banned or at least capped at some level? For all people, obviously, since you're describing inheriting wealth as being a sponger.
That's ignoring royalty-related tourism. Which shouldn't be ignored, since it's very real and brings in boatloads of money. Tourists don't go to see Buckingham Palace because it's pretty.
In any case, becoming a republic would obviously be more expensive because we'd have to pay a huge salary to the new head of state and we'd incur significantly higher expenses because we'd had to provide security to every living head of state and we'd be getting a new one every few years. We could end up with a dozen living ex-presidents each of whom requires a high level of security for life. All that in addition to the same expenses we have now. Diplomatic costs, building maintainance, transport costs, etc. If the head of state from another country comes for a visit, we can hardly put them up in a Premier Inn and give them a bus pass for transport (although it would be funny to see the response to that proposal).
I've joked that I'm going to stand for election to the city council with my election campaign being a promise to waste people's tax money on beer and strippers, because then people will vote for me on the basis that I won't waste it as badly as the current lot have done. People laugh because it has some truth in it. Maybe politicians aren't the biggest spongers, but many of them must be well up on the list.