I quite like this idea.
If you wanted to go down the route of building the call graph for the entire binary (as the others have assumed), then you'd want to make sure you cache the result and only rebuild it if the binary has changed.
You could probably write an extension for IDA to build this cache instead of writing your own code for it.
Alternatively you could just write a thin function that takes a function pointer and returns a list of [non-virtual] functions called by it. Then you can use this in situations where you know the result will be meaningful.
I've written a basic
CFG parser which can be used to find the end of the function and could output all calls with only a tiny change. It embeds libdisasm which appears to be reasonably lightweight.
Let me know if you want me to dig it out. If the disasm lib turns out to be a bottleneck (unlikely) it wouldn't be hard to write a custom version for your needs.
Something to be aware of are is the massive possible difference between the linux and windows binaries. Calls which appear once in the original code, could appear multiple times in the assembly or not at all, and this would be entirely compiler specific.
tl;dr