I wouldn't put live rock or algae in a QT tank. CP and Copper would kill the algae and inverts, and cause the water to foul.
As far as biological filtration, biomedia is cheap enough to keep a spare bag in your reef sump to stay seeded with bacteria. Heck, even crushed coral works. If I decide to empty the QT tank, I make sure to have a fresh bag or tupperware with some biomedia in my reef. Then in the future, I can easily spin up my QT with seeded bacteria if there's a fish I want to buy. I never return the biomedia back to the reef sump if it's been used in a QT. It's too risky if it happens to leach medications like copper, and like I said biomedia is cheap.
I would also suggest adding a seachem ammonia monitor: https://www.seachem.com/ammonia-alert.php
I would also advocate treating with CP and Prazi at same time. This covers the most common ailments: Ich, Velvet, Brook, Flukes, and Worms.
Yeah I agree with your statement if I were using CP or Copper for my QT, but I'm not using those 2 meds. I like your setup as well. I have not had to use CP or Copper yet, but if I do I would use your method for biomedia. Thanks for sharing. I have always wondered how I would keep water quality up if I had to treat a fish with copper when setting up a quick Sick tank.