QT?

Absolutely do not need to run it 24/7.

The fish that needs to be QT the most are unfortunately the bigger ones that need more room too. Tangs, angels, puffers. Your smaller fish like gobies, wrasses and so on usually dont have near the problems. So a bigger tank, or even a stock tank works well.

Unless you are going to QT a wrasse, just use a bare bottom tank, cut of pieces of PVC works good as hiding places. Heater, air stone, and a hang on back filter and away you go. If you have a sump, it is a good idea to put the HOB filter pad in your sump to collect bacteria. When you are done with the QT, throw that pad away and put a new one in the sump for next time.

Most of your bacteria is usually colonized on surfaces, so using tank water will only give you a small benefit.