Calculus class simply provides a method for testing how good your algebra is. It's an elaborate algebra test. The stuff where you use calculus is the calculus test, etc. etc.

I know of a specific technique for teaching algebra - write down the principle used to justify each step in a derivation/solution - that will teach algebra cold but it "costs" too much so we don't do that.

I've heard at least one "officer" ( like dean ) level academic say "We use calculus class to keep the stupid people outta med school."