First of all, what makes "monoid" a "complex" name? Is your complaint basically about terminological aesthetics?

I'd say no to your question. I've linked an article elsewhere in the thread that to me shows pretty clearly that monoid is a useful and generative concept.

On a more basic level, I personally really enjoy taking inspiration from math and logic into programming. You mentioned composing programs in a way that is safe and correct; I think the algebraic approach to programming is a really excellent and deeply fascinating way to approach that goal.

IMHO, naming things sometimes only makes sense in a specific, wider context. Thus, using a domain-specific jargon to name a simple thing like an associative operation with an identity does not make much sense outside of the domain (in this case, abstract algebra).

The extreme example of the same nature is the notion of "magma" that finds some use in algebra. Would you use this word to describe a function with two arguments (that have the same type)? There's nothing to be gained by doing this outside algebra.

I guess the underlying discussion here is about viewing programming as a kind of applied algebra, which is common within functional programming and not so common in other traditions.

I happen to find that view really fascinating and generative, but I don't blame others if they aren't interested.

I also wouldn't insert the monoid concept into a codebase that isn't Haskell or doesn't already have some alignment with algebra, because it would seem weird... and Haskell has features (typeclasses and purity) that make monoids really nice to use.

I also don't generally do language advocacy, and I have a great respect for the diversity of ways of thinking and learning. But I also wish people wouldn't dismiss concepts that other people find useful and good just because they don't immediately see the point.

In other languages this kind of problem is typically solved with an explicit accumulator and a for loop. Plus a little crutch in places where higher order functions would really make sense :-)