there is really no natural, real world example of algorithmic recursion, and so the concept is alien.
I object. Recursion is a fundamental property of just about any natural language. You can make sentences infinitely long by recusively adding attributes, subsentences, clauses and whatnot.
I do agree though that the fact that many instructions are expressed in a steap-by-step manner may influence the way we think about algorithms - but it works the other way around too: If we think about algorithms as stepwise instructions, we may forget to look at them in a declarative manner, which can make such programming concepts harder to grasp if you are accustomed to the imperative style.