I don't think that the Open/closed principle as originally presented allows the interpretation that final classes can be extended through injection of dependencies.
In my understanding, the principle is all about not allowing direct changes to code that has been put into production, and the way to achieve that while still permitting modifications to functionality is to use implementation inheritance.
As pointed out in the first answer, this has historical roots. Decades ago, inheritance was in favor, developer testing was unheard of, and recompilation of the codebase often took too long.
Also, consider that in C++ the implementation details of a class (in particular, private fields) were commonly exposed in the ".h" header file, so if a programmer needed to change it, all clients would require recompilation. Notice this isn't the case with modern languages like Java or C#. Besides, I don't think developers back then could count on sophisticated IDEs capable of performing on-the-fly dependency analysis, avoiding the need for frequent full rebuilds.
In my own experience, I prefer to do the exact opposite: "classes should be closed for extension (final
) by default, but open for modification". Think about it: today we favor practices like version control (makes it easy to recover/compare previous versions of a class), refactoring (which encourages us to modify code to improve design, or as a prelude to introducing new features), and developer testing, which provides a safety net when modifying existing code.