If you Google r/copenhagen PostNord you will see countless horror stories, mostly focused around delivery drivers simply refusing to do their job by purposely not delivering packages. I doubt freeing them of their obligation to deliver letters is going to improve things.
We also have the full might of the state behind them who will happily charge you multiples of the value of your item coming in from out of country because they "inspected" it.
People in the US don't understand how good they've had it (well until very recently with tariffs), as you could get any item you wanted delivered to your doorstep with no additional fees and better customer service at a fraction of the price it costs us.