The article already answers this:

"When the purchases are linked to a household, it will be possible in the consumption statistics to analyze socio-economic and regional differences in consumption, and link it to variables such as income, education and place of residence."

That can still be done with anonymized data. It is not necessary to associate purchasing habits with national ID numbers to perform the analyses you listed.

I fail to see how you can get this kind of data from anonymized supermarket receipts? Entirely different data collection methods: sure. But the entire point of this is that was too difficult ("time-consuming and error-prone", according to the SSB).

Issue national ID cards that contain a private key. For each citizen, the government would encrypt a mapping of their national ID number -> anonymized ID ("anonID") using their corresponding public key. The anonID could only be used to look up anonymized demographic data, updated when new IDs (and thus new encryption keys) get issued, once every few years. When checking out at the supermarket, your national ID number and private key would be used to generate your anonID on the spot, under which your purchases would be recorded. Demographers could thus freely query mappings from anonID -> demographic info/supermarket purchase history, without revealing anyone's actual identity. Without knowing one's private key (which is embedded only in their national ID card), it would impossible to freely map national ID -> anonID.

I get a feeling that this is a roundabout way of simply anonymizing the ID in the data when it is collected, as have been done a lot in studies. The problems with this is that our behavior is unique enough that is it often possible to find out who you are (or what demographic you are in for advertising purposes) from your actions, no unique identifier needed.

One example of this is when our national newspaper (NRK) did an investigation[1] on "anonymized" GPS data, and could easily find the identities of the persons they belonged to.

[1]: https://www.nrk.no/norge/xl/avslort-av-mobilen-1.14911685