What is the real benefit of creating a new programming language? It is highly unlikely that you are going to actually use it.
In short, how will the process of creating a new language make you a better programmer?
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You will understand the decisions behind language design and garner a better overall understanding of the compromises made between readability, performance, and reliability.
Your familiarity with concepts such as recursion, closures, garbage collection, reference management, typing, data structures and how these things actually work will increase. Most programmers will utilize resources and language features better.
Similar to the way we learn new ways to code solutions when we use other languages, when we write our own languages, we explore new ways to create solutions. See Metaprogramming. Contrary to the what the question suggests, Domain Specific Languages are used in many environments.
If you’re writing a compiler, you’ll learn more about how computers work than you ever did before. (Depending on your goal, perhaps more than you intended to learn)
When I wrote my own sort routines in school, even re-implementations of good ones, it really drove home some of the weaknesses of some of the algorithms.
In short, there’s an order of magnitude of difference in a programmer who knows how to use tools, and a programmer who knows how to make tools.