To rephrase what I mean: I disagree with the idea that we can explain all technical concepts in non-technical way, which OP seems to support. I don't think we can get much better with teaching monads than providing actual formal definition plus motivating examples. I simply believe monad is too abstract and we can't have a nice analogy similar to the one OP provides ("Functors can be broadly explained in terms of containers..."). In my opinion the "platonic ideal of a monad tutorial" is more or less the (semi) formal definition of monad + some motivating examples. This is also something that cannot be understood if you don't have proper background (which is understanding simpler typeclasses like monoid and functor).

I also would not call monads a pain point to be fair.