That would be a fine answer, but for the fact that other currencies like the rupee (₨) that are "just letters" do have their own codepoint. Being made up of two symbols doesn't necessarily make something not a symbols, in semiotics or in Unicode.

In fact this is one of the root problems, there are plenty of Unicode symbols you can make out of others, either juxtaposing or overstriking or using a combining character, but this isn't consistently done.