Wouldn’t flash cooling inside a freezer ice cube box be as effective as an ice bath?

I was a mechanical engineer. The heat transfer will be much quicker in the ice bath because you will have full surface contact between the meat and the water, even into all the nooks, cracks and crevices of the meat. This is not possible just putting it in tghe freezer. Water is a great conductor of heat. Air is an insulator. You will have parts of the meat surface insulated by air.

There are other, greater, problems with your suggestion in lieu of the ice bath. When is the last time the freezer box was sanitized? Probably never? Where does all the melted ice water go? Into a puddle at a low spot to refreeze? You are bringing odors into the freezer box. The meat is picking up odors from the freezer box even though you might not be able to smell them or are just aclimatized to them.

I don't think that'll be as effective, no, unless the freezer itself is extremely cold, ideally with good air circulation.

A freezer ice cube box isn't going to actually be making full contact until it's melted enough to turn into an ice bath anyway. Until then, it'll have some amount of water melting, dripping, and refreezing, and ice in partial contact with the food. In contrast, an ice bath makes full contact with the food immediately, and it has enough liquid to circulate and make sure that there aren't warmer areas near the food.

Also, ice baths are usually used to rapidly chill food, not to freeze it. By the time a freezer manages to fully chill the food, the outer layers are going to be frozen, a pretty undesirable result if you just wanted chilling.

A bit of a side note: "flash" cooling/freezing refers to a method that cools/freezes quite quickly, by circulating extremely cold air across the food. (Sometimes it's also used to refer to the fastest freezing you can get at home, placing very small pieces of food in the freezer.) Putting cooked food in a freezer with ice cubes isn't really in either category.