It's not that you couldn't do that, it's that polymorphism (in the interface/virtual functions sense) is only one of several paradigms for abstraction/code reuse in C++. And it is on the higher side of runtime cost among them.

Also, the type system in C++, despite all the template stuff, is not actually very good for serious functional programming. For example, when taking a function, there is no generic way to specify its signature in your own signature (and no, taking a std::function is not generic). `require` goes a long way though nowadays.