In the Netherlands the situation wasn't too far removed from the situation the UK is in now. The postal codes are managed by a private company (PostNL), and while the details are scarce and hard to find there was a fight between them and the government party responsible for managing addresses over who got had the rights to the postal codes data (see [1] for the current truce).

[1]: https://www.geobasisregistraties.nl/basisregistraties/docume...