That about matches my fuzzy understanding, but the big picture is the struggle. Like as submitted in a comment here about the venerable for loop being rooted in calculus, it makes sense when it's explicitly pointed out, but I haven't established a framework to draw those connections intuitively.
To generalize further, given a solution where the use of calculus is explained then that isolated example is comprehensible, but given a problem there is nothing that sparks a "I know, I can solve this with calculus!" I don't feel the same way about other mathematical disciplines that I have studied, even those of which I have spent far less time studying.
Perhaps it's simply harder to understand than other areas of math, but then I think that goes against the idea that is easy for kids to understand.
To generalize further, given a solution where the use of calculus is explained then that isolated example is comprehensible, but given a problem there is nothing that sparks a "I know, I can solve this with calculus!" I don't feel the same way about other mathematical disciplines that I have studied, even those of which I have spent far less time studying.
Perhaps it's simply harder to understand than other areas of math, but then I think that goes against the idea that is easy for kids to understand.