India developed its own payment network called Rupay although adoption is a bit slow among the masses. Denmark should create its own network.
In addition, the dankort is strictly regulated to the benefit of consumers which the banks dislike because it limits how much they can charge when you use it. They have an interest in pushing people to visa or mastercard or their own mobile payment solutions which don't have the same restrictions. The payment processor itself is developing their own alternative to compete with the dankort which they are mandated to also implement. I don't think they provide bad dankort service on purpose but it's a concern that good service is actually against their own economic interest.