That's essentially every instruction though. You can't write a program that doesn't access memory for example, and every memory access is nondeterministic in wall clock time.
In the crypto example, the backend would have to be sophisticated enough to know when the same addresses would be accessed every time, like bitslicing in AES. [1]
The devil absolutely is in the details. This is why I say Yao's capabilities on this front are unproven.
[1]: https://www.bearssl.org/constanttime.html#constant-time-in-b...