Related note: Strang's essay on the imbalance in education in favor of Calculus over Linear Algebra is (in my opinion at least) a great read, for those interested in the pedagogy of mathematics.
He does more with some chalk and a big black board than any modern courses using fancy presentation technology.
[1]we followed Huffman-Kunze https://www.amazon.com/Linear-Algebra-Kunze-Hoffman/dp/93325...
For example, if there's a certain probability of people with cancer getting a positive test result, what's the probability of a positive test result meaning you have cancer? Too many people absolutely cannot approach that problem in any intelligent fashion.
(Side note: More classes should accept "there isn't enough information to give a coherent answer" as a correct result.)
It's a matter of focus: The point isn't to derive statistics, any more than the point of a first semester course on differential calculus is to derive the real numbers and the infinitesimals. Calculus isn't useless, it's just not as useful unless you go into specific fields.
If you don’t know calculus, someone has to tell you the formulas, which will seem like mysterious completely arbitrary magic. Memorizing them will be a pain in the butt. When you try to use statistics you will make small mistakes which will lead to wrong or even entirely incoherent results, but you won’t notice because you’re just following a recipe you don’t understand.
Of course, to do real statistics you need linear algebra as well.
There are also tons of very complicated advanced calculus and differential equations concepts that have direct "discrete" analogues in linear algebra, and this become glaringly obvious when trying to say discretize and solve a partial differential equation.