the issue is, rapid cell division is a very dangerous thing, and just telling cells to divide means certain cancer. "Good" healing magic would have to either prompt the body's pre-built directional systems to speed up to match the cell division, or understand exactly what is needed and be able to stop mutations before they spread too far in the duplication. We do not have enough knowledge in the game universe for the latter, and I have no idea how we would do the former without much much more knowledge.

However, that is not exactly true, because we have established with Skittles that someone does not need to understand how a magic works, though presumably the person who "created" the spell understood how it works and somehow makes it work automatically on casting. Therefore, I  would give the hypothesis that healing is currently only possible through ancient spells crafted by lost knowledge, or at least by scholars who have spent their entire lives trying to understand the way the body works and then turning that knowledge somehow into a spell.