Just to clarify. There is at least one chosen and contractually bound Mail Service provider in Denmark. Their terms are set in public tenders. The old state owned company - Post Nord - basically decide not to compete for the contract. A newer company - DAO - won the tender. What this means in legal terms:

Under law: DAO must comply with its postal permit obligations (nationwide service where offered, pricing transparency, quality monitoring). But there is no absolute legal universal delivery duty for all mail anymore.

Under government contract: DAO has a specific binding duty to deliver blind mail as defined in the tender it won - this is a contractual obligation, not a general statutory duty for all mail.

Be mindful that in principle the service provider could chose to not cover certain parts of the country. That has to be clearly stated in their terms of service. The Danish government are expected by the public to continue to subsidize delivery to people with special needs, in the contract identified as "blind mail"