Only one problem: "false" doesn't mean the same thing as fake. And since academics have this terrible obsession with accuracy and precision, "false" is absolutely the wrong word to use for fake handbags.

One might use false in a phrase like "false bravado" rather than "fake bravado", but that's because "false bravado" is about disguising authentic cowardice, whereas "fake bravado" would be closer to "imitation bravery" which doesn't really make sense.

Word frequency analyses might work for bots or for writing clickbait. But if you want to write something truly accurate, you can't beat actually knowing what lots of words mean and choosing the ones that best model the thought you're trying to communicate.