You're kind of arguing that you can't walk without studying kinematics.

im not though. I don't think you need to know measure theory and understand how to formalize probability in terms of sigma algebras to do professional stats.

But I would be very skeptical of a professional data scientist that doesn't understand things like derivative, integral, limit on an intuitive level. I don't know how you would understand distributions without that knowledge

R is not exclusive to professional data scientists.

Sure thing, you may be calling a function that does some regression or something, but you aren't "doing calculus" when you are programming that in R.

Are probability and statistics really practically based on calculus? Most math curriculums do not have a calculus requirement to take statistics.

for actual understanding, yes it is. The most basic important results, the law of large numbers, and the central limit theorem both require calculus to understand.

if you make a class without calculus, it is essentially just a bag of tricks and surface level understanding

rho(x) is the probability density function, and it better sum up to 1 for all possible values of x.