My treatment tank is about 25g, so for the best start, I'd use new water. I've never used a treatment tank before, but I now put the fish in, treat with a standard dose of CP for a couple weeks, and transfer fish to DT. I would then empty it, give it a wipe with a towel, and leave it until I get another fish. Repeat. I don't want to maintain a running tank as a q tank, as I don't regularly purchase fish. Since I treat for ich/velvet/brook regardless, I'm not worried about spores.
Bringing a new fish in, I want the cleanest water to start.
If you Q fish and don't treat, I assume there are no cysts to worry about. If you previously treated with copper, then you either mix dosages going forward, or you use carbon to remove it. Waste of perfectly good carbon
Ultimately a personal choice, but for me, I'll just make clean water.