Calculus is also a requirement for statistics and probability. You simply cannot meaningfully talk about the latter without referencing the former.
In the land of the blind the guy with one eye walks everyone off a cliff.
What happens is you learn numerical approximation methods and then recreate the tables with human 'computers', like we used to do before electrical computers came into play. Or create mechanical analog computers like they did in the 1800s or greek times.
How would the typical person go about calculating the normal distribution by hand? Are we going to call everyone blind because they haven’t memorized e to arbitrary precision?
IDK, what does R do?
I also think you could and should start by teaching probability and statistics and using that to introduce calculus as and when it shows up naturally, rather than teaching calculus in the abstract first and then showing the applications much later.