There is nothing complicated. There is no need to "extract". When the original file doesn't have a second UV, then this information doesn't get written to the FBX.

But it makes on the other hand trouble to use a "native" format that doesn't support all needed features. It is simply no good idea to use "the native engine format" in all cases and under all circumstances. There are thousands of engines out there. Can you imagine the chaos that would mean when they would all throw their native engine format onto the table? There is simply a need for a more general file format. A file format that covers most of the needs. And FBX is one of them. FBX is your "standard game oriented file format". X is another.