Forth isn't an esoteric programming language. The word “esoteric” has a specific meaning in this context.
Forth is not that.
It was designed as a practical, stack-based language for embedded systems, instrumentation, and real-time applications. It emphasizes simpilcity, extensibility, and efficiency, and has been widely used in space missions, robotics, and hardware control. While its stack-oriented, postfix syntax can look unusual to those used to C-like languages, its purpose is entirely practical, not experimental or artistic.
It is most assuredly different than typical languages, but I don't think that means "esoteric". As an industry, we're sort of lost if "esoteric" means anything that doesn't look like Algol.
I'm of the opinion that one must write a forth to grok forth, and I'm far from alone in that. However, I'd not quite call forth itself esoteric. But to many, it's a language family... of which most of the members are esoteric inasmuch they only have a single user.
* shout-out to my friend whose forth supports lists, hash tables, and structs through syntactic sugar... https://github.com/cstrainge/sorth
But more to your point. FORTH was used in a time when the predominant mode of coding was to construct more complex programs from less complex programs, so application developers usually got their hands dirty with some lower level aspects. That is... the application programmers chose the lower level abstractions they wanted to use. Now that we're beyond that and have, as an industry, decided that van Rossom and Latner are the only people who are allowed to define low-level abstractions, it's a lot harder to do that.
(Again, file this one under "old man yells at cloud.")
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Maybe it's best to think of FORTH as a DSL construction kit. Lisp is kinda-sorta the same way. As you point out, it's super easy for someone to develop DSLs that require coders to understand not only their application domain, but also how the language and it's underlying hardware abstractions operate. And when you're using someone else's DSL, you have to understand how they thought about the problem domain. And we stopped teaching how to analyze that in the 80s.
Also... +1 on the "you've got to write it to understand it." And in the 80s, the documentation wasn't super. Leo Brodie's book was great to get you started, but understanding things like ' (tick) and how to program in "idiomatic forth" was a challenge. So I would add, "not only do you have to code FORTH to understand FORTH, you also have to rip someone elses' FORTH program apart to understand the more advanced bits." -- I could be wrong about that today, it's been a while since I did a survey of FORTH documentation.
It isn't how we teach math in the two countries I've lived in. Lisp is just as weird. Many people see a mathematical expression and panic. A level up from them, people see a mathematical expression in some source code and expect it to respect the symbol precedence that they were taught in grade school -- which they can "understand" without knowing how the language parses and abstracts all that away. And maybe their understanding is flawed but they can survive as programmers for decades without ever going deeper. Lisps, FORTHs, etc., don't allow you to proceed without understanding.
> Here's the definition from the esoteric programming language wiki, which is a lovely resource for anyone interested https://esolangs.org/wiki/Esoteric_programming_language:
> "An esoteric programming language is a computer programming language designed to experiment with weird ideas, to be hard to program in, or as a joke, rather than for practical use."