Well, if you have only half-wit PHBs, it might be better to restrict their budget - they wouldn't know how to hire good people anyway.
Only question remaining: Is it half-wits all the way up? Knowing the company... yes.
@PeterW Scoring a good boss is better than winning a lottery. The odds are longer though. 30 years at the same establishment and 40 years working for a living, I lucked out and got one competent boss. She cured half my stress symptoms just by keeping the PHB types out of my hair. What was left of it at the time.