You forgot:
2b. LLMs are empowering bad actors to exploit loopholes and collect benefits they're not entitled to.
The assumption from a lot of commenters seems to be that these are all legitimate claims and appeals, not a gold rush to get money from the government while the getting's good. In the end it will be the good faith actors that suffer - both those relying on these benefits to survive who will have to jump through more hoops to prove it and those funding the system with their taxes.
Having older parents and watching what my grandparents went thru long before LLMs I just don't worry about the poor old state that much.
The political zeitgeist is to always blame the "bad people", the "welfare queens" and the "undeserving" as the problem with the system. But never the complex system that's seemingly designed to benefit things like corporations extracting as much wealth from the system as they can. Or politicians ear marking the money for things they want to do, rather than the people that put the money in the system.
So, yea, your reasoning just really doesn't hit me in the heartstrings at all.