TYPO3 Core

I also have this problem, but with export in TYPO3 8.7 and TYPO3 6.2

Exporting files and having them in .xml / .t3d / .files folder does work - at least in v8 and v9 (and i guess in v7, too since not much changed codewise in this area, but I did not specifically test this): I just played around with that for a while for the ext:introduction extension.
Make sure you enable the sys_file* tables in "Include relations to tables:" and do NOT include them in "Use static relations for tables:", also do NOT use [All tables] for this one.
This way i was properly able to have fal files from tt_content and other tables in my export - there is a uid shift on import again, but that is a different topic.
I'll close the issue for now. If you still think this is broken, please reopen / create a new issue with more detailed export configuration details, maybe even by submitting a preset dump.