That's generally how I run my settings. Low-level magic, to keep people healthy and provide low-level utility, is ritualized and commonplace. I don't really like to imagine my PCs in worlds full of disease, foul odors, and rampant death from infection and childbirth, so background magic explains that away.That's pretty much what I do. Some people may not even realize they're using magic, but the blacksmith knows that if he sprinkles in the right powder at the right time and chants a song to the metal, the metal is stronger and rust resistant. The local healer has poultices that work similar to antibiotics. The milk maid hums a tune and the milk stays fresh longer, the Keeblers really do make magically delicious cookies to dip into that milk and so on. The PC classes are the soldiers of the world with specialized training and equipment that people that are not on the front lines don't need.
It even permeates basic biology which is why people heal up so quickly, even if they don't realize that there's anything unusual.