The amount of execution time is a simple public parameter of the system. These schemes require reducing the verification program to a circuit in advance, so it

The amount of execution time is a simple public parameter of the system. These schemes require reducing the verification program to a circuit in advance, so its execution time is already fixed by virtue of that translation. (In practice the existing implementation is not using constant time cryptography; and so it could have timing/cache/EMI side-channels; but this is "just engineering")