Measure your baseline, pick good metrics, build human-vetted ground truth, then work through false positives/negatives starting with the most egregious/surprising. Start in shadow mode until the system is clearly better, however you must define that to ensure trust/buy-in.
For example supporting you spend 10x and hire a bunch of the smartest people around to run this process. Do you agree that you could decrease wait times?
You can think of this in terms of labor productivity if it’s helpful. It’s not a fixed value. The hypothesis is that if AI can increase the labor productivity of claimants, it can increase the productivity of the administrators too.
You apply for your permit or whatever and the AI instantly denies you, so you start over and pull the lever again and this time the AI's random number generator comes up 777 and you get your permit.
Then the house can tune this for either reducing red tape (e.g. pulls are free) or favoring the rich (you have to pay a fee for each attempt so only the poor have to take the L once they run out of pocket money).