a tank with live rock usually contains high nitrates and a high level of bad bacteria and viruses.
This is quite false, however uncured live rock may have some pretty nasty stuff on it, but you buy it cured to avoid that mess. Tanks with live rock are less likely to have a build up of nitrates because there is natural growth that eat waste including nitrates. Nitrates are dependent on how well you keep to the tank from excessive food, over population, and keep proper bio filtration, and basic upkeep.
Putting new fish in a QT for two weeks greatly reduces bad bacteria and viruses from entering the main tank. This is so with or without live rock.
With proper supplimentation and varied food sources there is no reason y angel fish cannot live full and healthy lives without live rock.
Angels do not live very long in tanks without live rock. These animals can live 20 years, maybe more, but they'll never reach that potential longevity in captivity without having free access to the natural growth on live rock. There are remnants of corals and several types of algae as well as pods among live rock that they require for longevity and there's only so much one can suppliment with. Angels are coral eaters and need that protein. Sponge fortified foods only help so much. The variety of coral protein available to them in a tank they can freely graze on live rock will give them that variety.
Copper is becoming ineffective. In fact, most of the parasites responsible for serious diseases have become copper resistant. These are tough buggers. Personally, I FW dip most marine fish, especially angels for external parasites and just use a simple antibiotic for the wounds left behind by the parasites. As of getting to a fish when it needs to be put into a QT, there are fish traps that are effective to your enthusiasm in catching the fish...LOL. They can be fun. Anyway...
A natural tank will help heal a $300 angel and with less stress involved to both you and the fish. It also prevents stress related diseases common in marine fish in captivity. Any of our fish in a FO tank that needs a bit of extra care go into a reef as part of it's treatment and it works most of the time. Right now I have a tang being treated in a reef. No meds. Just a natural environment. He is healing. He started to come down with inline recession, which is a nutritional imbalance problem common in tangs. I recently had a juvenile blue face angel with a slight bacterial and he went in the tank and healed. No meds. in the tank. Just a couple of FW dips, a squirt of wound control or bio bandage and a reef tank. I've lost more fish treating with chemical based meds than I ever have using natural methods.
Bottom line, it's your choice and all I'm providing are testimonies and info. of successful treatments without the use of chemical based meds into a tank. Wound control and Bio bandage is the most many get for chemical treatments and it goes directly on the fish instead of in the tank water. Just thoughts to ponder on.