This concept completely fixes inequality and fully replaces all forms of social welfare - no more wasted potential because a smart person is born in a bad environment due to genetic lottery. Advantage from growing up in a rich family would shrink to the point of irrelevancy. Investors would filter out ghettos in search of high iq kids to buy their shares early. No more need for public schools - because everyone would get the quality they actually deserve, all paid for by private investors. Same would apply to literally every form of social welfare that exists anywhere. Right now there's no market pricing of people at all - everyone either gets less than they deserve, or more, with the fair outcome statistically borderline impossible. The outcome is a horrific waste of human potential.
I think effective tax rate would go way down - because bidding wars on people would reduce it to the market rate, and given the increasing global abundance of capital, I'm pretty sure that's going to mean low single digit taxes (ie. selling only single digit percentage of ownership).
While the end result would be a utopia, it's hard to see how it could become the norm anytime soon. The concept directly takes power away from politicians, so to become the norm a large scale collapse of the state is required. Perhaps it needs a completely new environment - like space colonies in O'Neill cylinders, in which case we're sadly centuries too early.