You can parse the words in my necessarily oversimplified description, and I will stipulate your vastly superior abilities to convey ideas in a manner that meets your standards, but the essence of my point remains. I’m only trying to help the OP understand some of the reasons for the EC.
Include me among those annoyed when the pointless distinction between democracy and republic is interjected into a debate.
For one thing, it’s wrong: Google’s dictionary defines democracy as “A system of government by the whole population … typically through elected representatives.”
For another thing, it’s just silly. Are there any countries which have a “pure democracy”? In The Pitcairn Islands, “the world’s smallest democratic country”, representatives are elected despite that the eligible voters could fit into a smallish room.
Which you can do perfectly well using proper terminology, I would think, at no cost to your point, or to your self-expression. 
As for the issue of “democracy”, since the Greeks managed to utilize actual Democracy as a method of government, it’s rather churlish to assume that it cannot be used as such in the modern world. However, if you wish to discuss “representative democracy” as the type of system employed by the US or England, I won’t quibble with that; I prefer to simply use the term “representative” as an adjective modifying the source of power to accomplish the same goal (hence my use of “representative republic”). It is still the case that Frisco’s terminology is incorrect, especially by attempting to contrast the words “democracy” and “republic”, which are quite definitely NOT interchangeable, septimus, even using the definition you quoted, which has not one thing to do with the definition of a republic.