I was just replacing our dishwasher with a new one, and I noticed something...
First off let me tell you in the past I have always swapped stuff like this myself, but when we moved into this house we were just too busy and I didn't have time to do everything. I let my wife hire a plumber to install the dishwasher we brought from the old house and move her fancy toilets.
Anyway, I pulled the compression nut off the water supply line and it was wrapped in pipe dope... over top of teflon tape... AND there was more pipe dope under the tape. I stripped all that crap off the fitting with a wire brush and installed it in the new dishwasher. Tape on the tapered pipe thread into the machine, and nothing on the compression side from the supply line. Amazingly it work just like it was designed.