I see this as a good thing. It means that we'll (hopefully) get stricter security revolving around using these numbers. It'll no longer be enough just to yap out a 10 digit number to "verify" you are who you say you are. We already have a (albeit heavily critiqued) national 2FA system in place (MitID).
We'll have to start treating the CPR number as just a username, instead of a password. It should never have been "secret" in the first place.