Pragmatically speaking, I'd advocate cutting square cookies and embossing/icing seasonal designs/motifs on the top.
But... is it really Christmas if the kids don't get into fights over who gets the reindeer-shaped cookie cutter, and who gets the star? And this research is from a Danish university, Danish Christmas cookies don't have icing. We only get to express ourselves through the shape.
> if the kids don't get into fights over who gets the reindeer-shaped cookie cutter, and who gets the star?
This, in comparable situations I have witnessed, should not be a problem. The kids should be able to fight quite easily over nuances such as depth of icing, area of icing, colour of icing etc. And in the case of embossed designs, who gets the star motif and who gets the reindeer. Fighting among children is guaranteed to be preserved at current levels under my proposed system; it doesn't upset the status quo.
> Danish Christmas cookies don't have icing. We only get to express ourselves through the shape.
This is perplexing. Perhaps a national education programme might be initiated - using Danish influencers on YouTube, promoting the use of icing and showing how it is made. (You'd start with water icing and move up to royal icing etc.)
Furthermore, one might use this cookie dilemma ("Danish cookies don't have icing") as a metaphor to address other fixed biases in the Danish psyche that might benefit from frank and open discussion.