It could work the other way around, ie if your close relations have stock that may affect your governing decisions and they refuse to commit to re-investing more generally in the event of your election, then you are prohibited from running for office.

Obviously there would be complications, but are you advocating society shouldn't strive to clearly separate governance of the public from private, conflicting pecuniary interests? I can't tell if you're dismissing the problem or saying there's a better solution ...

I'm mostly thinking of spouses, parents and children, and I think that a blind trust should probably suffice (you could own stock, just not have direct control over it).

The rule sounds fair for direct family members (wife, husband, children under 18, etc.).