I’m no expert so please bear with me.
Homomorphic encryption [1] allows you to run a computation in a tamper proof way so that if you run it you can prove you did it faithfully.
With that idea in principle you can write a script that uses the attributes from the last, say, 50 blocks as the seed to a random number generator and use that to generate your private key and derive a public key from there.
If this process is blinded from the machine running it (because all the computation is done encrypted and the machine doesn’t have a way to decrypt) then you can have the script do whatever it wants and sign a transaction addressed to the newly created address.
Then at the end of the script the keys are revealed so the machine can claim the UTXO (broadcasting it themselves).
Now at this point you can chain them. Write a script that seeds an address and then write another script that moves those funds according to whatever rules you want. No need to update consensus.