It's pretty simple.
The US is a constitutional republic, or if you prefer, a constitutional democratic republic. The "democratic" part is all over the place, however - some portions are direct, some are indirect, and some simply give lip service to the idea. The critical part, however, is "constitutional", which is what keeps the two wolves from deciding what is on the menu.
Ok so you're a constitutionalist?
I'm not particularly against the term democratic, but if you are against using it to describe the specific action of appointment I can accept the preference towards accuracy.
PS Sin taxes are a thing too... and just imagine the double jeopardy on suicide!