Denmark isn't a great comparison because it's one of the places in Europe with the highest cost of living. Also these regulations aren't just to do with
free range eggs but any battery farming facility.
You might be on to something, that you should have the right to cheaper food, even if it notionally means poisoning yourself.
The problem is though that you are not always in a situation where you can make an informed choice. Even if all the necessary information is provided at the point of sale (an exhaustive list of the details of the production of the food).
You don't always consume at the point of sale: You may be buying sandwiches or be in a restaurant. Perhaps you could have regulations about the point of consumption having to declare all details there. I can imagine that becoming quite tiresome in Starbucks.
If you have that, how do you enforce it? How much do you spend? How much time do you spend updating these rules to cover all the new permutations that an evolving market produces every day.
Effectively this has what has happened with eggs in USA by transferring the cost of producing clean eggs onto stores and consumers who must now bear the cost of refrigeration.
There is an environmental cost to all this energy used as well, in storage and transportation. Then there is food wastage because these eggs spoil more easily. So it's not even all about "your" choice any more ...
By enforcing standards at point of production it drastically reduces the amount of red tape required to ensure consumers get a certain quality product.