But how far does that definition of calculus go, on your hill? Is it being able to perform single-digit additions in your head? Rote memorization of the 1-10 multiplication tables? Remembering the squares of 1 through 25? Performing division of 7-digit numbers in your head?

I don't think that any of that is crucial to math education by itself, but having an affinity with numbers (rather, an intuitive sense of magnitude) is very beneficial to understanding the more advanced concepts. The open question (at least to me) is whether that understanding is nurtured best by calculus, geometry or Cartesian graphs.