A lot of good arguments in both sides, and yeah it seems like the Ideal situation varies based off what your goals are. We have decided to keep our cabbage in the bag to stay consistent with Prigozhin's original cabbage.

https://www.youtube.com/watch?v=YkkaS1blmjo&t=52s

This video recommends to keep it in a bag. And this is what I always do too. I don't remember it getting mold ever

If you need more tips, instead of cutting it, I peel off whatever amount of leaves I need. Keeps it fresh longer!

Question is underspecified. Are you trying to minimize the chance it develops mold, or maximize the length of time that it remains indistinguishable from the day it was bought?
For the former, store it in a dehumidifier. This should keep the mold away for a good hundred years, or however long you can keep it thoroughly dried.
For the latter, store in a plastic bag with clean paper towels preventing contact between plant and plastic.
You can also go in between - store in plastic + paper towels while keeping an eye on moisture, and if you see visible water partially open the plastic to increase air flow. Once the water is gone, close the bag again.

The main argument is IMHO humidity - sealed in bag => more humid conditions as all the water that leaves the cabbage condenses in the bag, and thus providing better conditions for bacteria/molds to grow.

@MartinModrak Absolutely.

@ian what if the bag has tiny holes?

@Odoacre What’s the point of the bag then?

@ian there's semipermeable bags that help keep some moisture and prevent the dry air in the fridge from drying out the vegetables too much

@Odoacre Cabbage already has many layers of lettuce that protect it from drying out. You'd have to be desperate to manipulate a market before buying a bag to put a head of cabbage in it.

@ian yes but fridges are too dry for proper cabbage storage in my experience. In cold countries during winter cabbage can simply be stored outside of the fridge (and maybe the house). They can last for months as long as they are stored in a place thats dry and ventilated and non freezing. Stored directly in the fridge however they dry out too quickly. Maybe something's wrong with my fridge but after a few weeks it's all brown and leathery

What is yes and what is no?

@ian fixed