if really there are no ways to be sure that under zk are not happening arbitrary not-determided things then it doesnt solve any problem.

Under zk it is possible to verify the correctness of the computations.

You still cant "manually verify" the crypto that bitcoin uses unless you have very big hands, you need other layers of functions and appllied math.

In some cases we have advantages with bitcoin; it is simpler "counting all the utxo and verify that all the bitcoin that exists are the number we expect" than "run complicated algorithms that do stuff with proofs and crypto materials and expect some output to determine if all is run ok".

But for the most part, the crypto bitcoin core uses today is verified by "run complicated algorithms that do stuff with proofs and crypto materials and expect some output to determine if all is run ok".

The difference is that bitcoin crypto is battle tested, zk implementations are not.

But zk doesnt change nothing substantial, it is just another way to apply complicated math to do stuff and have deterministic ways to verify the correctness of calculations.