Ehhh, that's the flaw in the logic. Holding a PhD doesn't necessarily make you better at anything other than strictly the topic of the PhD (and sometimes not even that), maybe only following arbitrary orders from senior figures.

Holding a PhD at the very least means you can spend a sustained long amount of time on (potentially) intractable problems and try to arrive at solutions for them. That's a good skill to have when...you've been elected to solve problems.