> In a good program, most of those checks are not coverable from the public interfaces.

If they aren't then you are defending against situations that can never occur. In that case the check seems unnecessary, and I at least wouldn't make it a priority to cover it. Also, those checks are usually simple enough that one can reason about them easily, again making it less of a priority to have tests cover them.

> The other problem is that finding tests that cover everything from the public interfaces can be extremely difficult. Most test suites don't achieve full coverage even of theoretically reachable points in the code.

Yes, testing is hard. That is not a reason to write more detrimental tests though.