What's the fire department doing for me, a citizen of my town who has not experienced any fires? Why am I paying for it?
The embassy is for maintaining relations with foreign countries, not just passports and birth certificates (and pricey notary services). That seems like a sideshow. When it comes to services for the public, they appear to spend most of their time dealing with visa applicants, based on the crowds and lines I've seen. They also do offer assistance for missing persons abroad; if you have a relative that goes missing abroad the embassy will investigate. That seems nice of them. I assume other developed countries' embassies are basically the same though.
I guess to fit in your analogy I live underwater?