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The way in which monads are monoids isn't really helpful for understanding them for progamming.

I dunno, it helped monads "click" for me at a theoretical level (they're just monoids in the category of endofunctors, what's the problem?) but by then I'd acquired a strong intuition of them already, so maybe it's not helpful for a novice. I'm pretty sure Applicatives help tho, LYAH seems to think so anyway. They sure would have helped me: the "Gentle Introduction to Haskell" was anything but.

Monads being monoids isn't very interesting in a practical sense - e.g. just because you can associatively combine steps in a program isn't very interesting. (We do it all the time when we extract a subset of instructions as a procedure)

I'd say monoids are more interesting, mainly due to implications for massively parallel algorithms and caching and how finding operations that fit the laws let you reap massive benefits in both aspects.

I've yet to see something as practically interesting for monads. Perhaps monadic parsers or STM qualify. What would you say makes monads just as interesting in a practical sense?

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