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There are absolutely no requirements in Danish law neither current or pending that requires a system to be "online" or "hosted".

It is not an explicit requirement - the new legislation just lists a number of things that are kinda hard to do without being online.

I am curious which requirements you think this applies to?

electronic invoicing is hard to do offline

The ones I listed.

I think the traditional standalone accounting software will be a thing of the past here after the implementation of the new accounting law.

Also cloud based accounting systems are probably easier to make money on.