forensics – File based background data eraser

I am making a series of python scripts for data overwriting. My current prototype creates a series of large files and simply fills the memory (using a different system for additional overwrites). Is there an advantage to overwriting the entire USB after removing all files rather than doing this in terms of protecting against advanced cyber-forensics?

This simple project will be exclusively for USB overwriting so keeping the system running is irrelevant.

By “background data” I mean data that is not currently occupied by another file.