People don't understand what monads are because they don't know what problem they solve.
This article has the same problem. It doesn't explain what problem categories solve. Well it does but the average reader doesn't understand the problem exists.
If Haskell's "Monad" type class were instead called "AbstractComputationFactory" or some other such intimidating technobabble, then when someone looks up what is the superclass of IO they might just think "oh, that's some weird detail, whatever, I might learn about that later." Since instead the name "Monad" is vaguely funny and appealing, people want to master that concept in principle before they even get "Hello, world!" to run in GHCi.
Of course people are free to focus on whatever they want, and we can talk about the possibility of improving the pedagogical aspects of Haskell, and probably university teachers have interesting things to say about that.
But there is no magic way to explain an algebraic concept that will suddenly make it intuitive and easy. If people want to understand them, they'll have to study. If people want to use them without understanding them on the conceptual level, that is eminently possible.
I myself don't understand monads and I've been using Haskell since 2005. I'm just not good at abstract algebra (flunked that class) and PDFs terrify me. However, even though if a mathematician asked me to explain monads I would be embarrassed, I can still use them and even define my own. That's because I've tinkered with them and acquired a know-how feel for the structure and what they are good for and how the patterns work—which is exactly how I've learned every other concept in programming.
Since most concepts in programming are ad-hoc, informal, and specified by hand waving, there is not even a possibility of understanding them at the level of mathematical rigor. What is an object? What is a class? Nobody knows. They just use them.
Or for that matter, the fact that it even is a problem, because it's easy to see that there are plenty of other programming languages with which people can do lots of productive things without ever thinking of the term "monad".