The "pay your bills" part gets tricky as IRS considers that a fringe benefit taxable at regular income tax rates. A corporation also is not eligible to deduce a certain variety of bills (e.g. dependant spending, medical bills over certain amount, interest on home mortgage) so it's mainly a way to increase the amount of paperwork and decrease the amount of eligible deductions with very little to show in return.
I am not sure how "make investments from your company" is just an overwhelmingly better option than "make investments from your personal account". Not only the corporation doesn't get a variety of tax advantages, such as 401(k), IRAs and Roth IRAs, there's an added burden of an additional K-1 for the investment vehicle.
Have you ever actually attempted any of the "obvious" optimizations you provide here? Has anyone ever used your advice for their tax planning?
Contrary to popular disbelief, folks at the IRS weren't quite born yesterday.