But numerical analysts really require being able to specify the semantics of calculations precisely in order to write libraries that mere mortals can use to get the approximate right answer.
A quick perusal of any numerical analysis textbook should convince you that order of evaluation, order of truncation, overflow modes, and the like are very relevant for being able to write a library that has the right order of error.
Something like Kahan summation will have vastly different results depend on whether intermediate calculations are done at a higher precision or whether the compiler is allowed to reorder expressions. In fact, an overly aggressive optimizing compiler will make Kahan summation simply fail [1].
If all you're doing is adding a few numbers together, by all means, you don't need or want to think about precise semantics. But if you've ever used BLAS or Numpy or any other math package, you very much depend on languages and compilers being pedantic as possible in spelling out how floating point gets evaluated.
