Can a stateful smart contract create a logic sig?

Yes, it’s possible as a logicsig contract account is just the hash of the compiled bytecode of the contract with some prefix.
In the past it was useful to create customized escrow accounts.

Now most use cases can be dealt with inner transactions.

That being said, I can see edge cases where it can still be useful such as Unique NFT ASA Implementation - #2 by fabrice

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