No, the shares can be directly transferred to a government-held portfolio. Come on, think for 2 seconds, my god. If you're going to rage like this at least don't come up with strawman issues that can be trivially resolved in 2 seconds of thinking.
Not to mention that the Norwegian Pension Funds holds $2 trillion in assets. UAE and KSA have ones over $1 trillion each.
And that's ignoring that currently an even smaller group of people owns everything, who don't even represent the public on paper. Quite stupid to assume that this is a better idea.