True. But if the system is implemented by a country this could be implemented using the law system and insurances.

For example, when each transaction is done, both parties might keep a cryptographic proof which they are required to submit once they are online again.

Failing to submit could result in a small fine (to encourage submission) and double spending which can then be detected could result in a large fine (or even a prison sentence), for example.

There is, perhaps, a privacy issue, just like with blockchain. But it's not more of an issue than online transactions.

I figure you can ‘solve’ it socially and legally by treating double spend while offline the same as writing a bad check. Recipients of offline transactions knowing the risk would limit it to small amounts and or emergencies.