That’s what a “tragedy of the commons” is though. The degradation of a shared resource (state capacity) by people acting in their own best interest.
The state using AI “to make bureaucracy instantaneous” is a tragedy of the commons. The experience is degraded because before you trusted your grievance will be heard, but now you might get auto rejected by an AI. It’s pretty much the definition of the phrase.
The stuff of many sci fi tropes - it seldom ends well.
A bit OT but there's a character in a couple of frank Herbert books - Jorj X Mckie saboteur extraordinary in the Bureau of Sabotage (BuSab). BuSab is a government agency responsible for conducting dirty tricks "in lieu of red tape" to help slow down and regulate the vast galaxy-spanning bureaucracy.
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).