What's the benefit of "opaque" pointers?
For background, my C code is almost entirely on microcontrollers. So I'm looking at it from that point of view. If you're talking about event-based applications running inside a full operating system, I've always stepped up to something like C#, so I don't have much experience with function pointers for that kind of work.
But consider the position of developer who implements a shared library that is distributed in binary form only. In this case, the benefit of opaque pointers for the development of a library is that the implementation remains private at the source level. One could, of course, reverse-engineer the binary but few people would do it.
If you define your structures in a public header -- and this includes C++ classes and templates with private members -- one can easily see the implementation and, with a few casts, start munging the guts of your objects and baking in a hard requirement on a specific layout and / or version of your library.
But for dynamic linking, this is how you avoid breaking ABI while maintaining forward flexibility.
They called this "modular programming" where "classes" were represented by opaque pointers and actions could only be performed on those pointers using the functions defined in the module.