C++ is designed for good performance. Solving ABI problems permanently usually means an extra layer of indirection, which hurts performance.
There are also concerns about what you can link against or not once you modify the ABI of widely used types. This is of real concern at least for closed-source software or software that just cannot be recompiled.
I am not saying it should be the right choice, some of that software is legacy. I just say this is a real concern.
As for the private function. You can use a pimpl and use a private (on the cop file instead of header) and use that, for example, in many cases. This keeps compile time down.