"...preferring "constitutional republic" to "representative democracy", as if they were different things."

And they are NOT "two different things" no matter how loudly anyone protests to the contrary. We elect our representatives and our POTUS (and sheriffs, judges, even dog catchers) in a democratic fashion.
We uphold democratic principles like freedom of speech, security in our persons and personal effects, prohibition against self-incrimination at trial, no state sponsored religions, and much more.

We ARE a democracy, a representative democracy enshrined in a constitutional republic. The two are neither mutually exclusive nor detrimental to each other, and athenian direct democracy is ancient history, tried once 2500 years ago.
So the only people who keep harkening back to such an old chestnut are people who are hostile to democracy.

"The Best of the Leon Russell Festivals" DVD