Programming languages take much more into consideration. Like ergonomics, backwards compatibility, user requests, etc.
Why should Relationship algebra have a pivot func? It doesn't. But a database engine might.
Compare relational algebra to Oracle/Postgres/My SQL for instance.
One scenario is when your goal is to make something new. Something, that would feel different and have different ergonomics. This is like inventing a Python when there are mostly C-style and Pascal-style languages.
Other is when you are interested in a particular behaviour of the language. Like type system. Why should you bother whether you write let x = 5; or int x = 5; when all you are interested in is its type. This is likely the case of this paper.