'LLMs to send birthday messages' is the latest fascinating example of 'a thing that is useful for governments and organisations being weirdly packaged as useful for households'.
So much of, e.g. anti-fraud is going to become easier and more effective the more of it we can automate it (a lot of it is just 'we got this bit of the state to talk to this bit of a bank which talked to this mobile phone company' which obviously takes a lot more time the less automated it is.
No - the Post Office scandal is not relevant here, that was about using tech for fraud detection, not speed. And the central problem in that case was the people and leaders who persisted long after it became clear the software was returning false positives.