Yes. You will never have a startup test of all the instructions used, in all the circumstances where they are used. Startup tests are useful for checking the presence or absence of certain advertised features, such as SIMD instructions. They are useless for buggy compilers and buggy chip implementations.

And, what would the code do if it detected such a bug? Abort, or run other code that works OK anyway. So, run that code all the time, and you don't need to try to check.