A computer on the other hand is utterly intractable. I'm not sure how that would help with unique, one off or under-specified problems.
If you want your bureaucracy to be more adaptable, I'd argue you need to give it more flexibility not less.
I'm sure several people on here would disagree with that, as there are plenty of people good at "convincing" computers to do things they shouldn't be doing, or to do things that their owners don't want them to. You just have to be more of a black hat, less of a schmmoozer....
I'd argue that even a hacked system is intractable though, as it still rigidly follows the rules no matter the outcome. That's usually what black hats are exploiting in the first place.
If the problem with bureaucracy is rigidity, then replacing human agency with computed agency would only exacerbate that in my opinion.
A (governmental) bureau is responsible for a delegated area of licensing (pre-emptive control), regulatory oversight (ongoing control), and "criminal" investigation (retributive action for violation), as granted by its enabling authority.
Bureaucracy is the discipline/science/art of managing a bureau, which isn't producing competitive market-action revenue (profits), so can only control efficiency by containing costs, which itself is an action that doesn't produce market revenue.
Oversight of a bureau (ascendant bureaucracy) exists solely to make sure some metric of cost containment and compliance with enabling authority is maintained within each bureau itself.
In short, bureaucracy is the regulatory management of regulatory management.
But as soon as you're trying to do something unique or one-off or under-specified, bureaucracy impedes more than it helps. Which is probably why large bureaucratic organizations often get out-innovated by small organizations with far less resources at their disposal.
Bureaucracy is a solution to a coordination problem that I would argue doesn't really exist anymore. Software is, in one sense, bureaucracy codified in mechanical form. It replaces and obsoletes human bureaucracy. The classic bureaucrat essentially applies a rulebook to his input information and passes output information to someone else. He is a human computer.
Even the evolution of war leaves open the question whether bureaucracy is an asset or a liability going forward. War is getting faster and more targeted.