Realistically the bandages thing is simply a convenient way to show that the person tried really, really hard to make the meal. Story-wise it's rare that you can show the person doing the cooking and struggling with it, but the bandages tell the reader all that happened. It's also used when someone spent a lot of time and effort making a gift they sewed or knitted.
Getting cut, even badly, while cooking isn't too uncommon though, even with professional chefs. I remember seeing an episode of Iron Chef where the challenger cut herself pretty badly. She basically put on some gauze, then wrapped her arm in plastic wrap to keep blood out of the food and kept cooking. Even if you use proper technique, dropping a very sharp knife, something easy to do with wet hands, can lead to getting cut.