The only situation where that makes sense is if you're not only good at whatever job you have, but you're an expert stock picker and you discover through your superior skill that the one stock with the greatest upside is..... your employer!
The argument against your POV is right in your answer: leaving RSUs as company stock when they vest is no different than a non-employee buying shares of that stock at the vest price.
If instead of getting $X in RSUs you got $X in 'bonus' cash every month would you turn around and put it right into your employer's stock? Probably not.
Regardless of how confident you are in your employer, most people's single biggest investment is their job. Correlating your investments and your regular income is making an incredibly narrow bet which is reckless unless you can see the future.