They would have access to IDs and whatever photos or real time video/audio is requires to verify. That's a big step towards building quite a large dataset for ID systems used for surveillance, for example.
There's also always the risk of not knowing who gets those documents later. The Dutch didn't think much of keeping detailed records including religious affiliation until the Nazis rolled into town.
LLM use is obviously much less politically charged today than religion was then (or ever), but that can always change, especially when an administration has already attacked said LLM provider as being something along the lines of a dangerous enemy of the state.
There's also always the risk of not knowing who gets those documents later. The Dutch didn't think much of keeping detailed records including religious affiliation until the Nazis rolled into town.
LLM use is obviously much less politically charged today than religion was then (or ever), but that can always change, especially when an administration has already attacked said LLM provider as being something along the lines of a dangerous enemy of the state.