It seems to me none of this is as clear cut as it seems. Government entities may hold shares in private companies, companies may act on voter's demands by accepting government grants. For some companies, government contracts are actually a main revenue stream - shareholders can jump up and down, if their supporters are voted out they will falter.
Corporations are still subject to law and ultimately under the control of the government. The current set of rules just gives them a fair amount of freedom to operate.
This only makes sense in a spherical-cow-in-vacuum world where government and business are somehow barred from communicating with one another. In reality, the "current set of rules" in many countries is a result of companies relentlessly trying to and succeeding in finding ways of influencing government. Political advertisements, campaign funding, lobbying, corruption, underhanded favoritism, countless other methods that are an amazing RoI for any business large enough to engage in it. Large enough corporations are resembling governments more and more in terms of value and power, and they use all of that power to endlessly try to bend the rest of society into serving their profit motive.
1. Not all companies are publicly traded, and they don't have to be
2. The 'voting' and 'steering' in a corporation is also completely dependent on money. The value of your 'vote' is proportional to how much money you have. This isn't a democracy or some sort of equal system that will converge on serving people, it will converge on serving money. I'm genuinely baffled at how "you get one vote per person" and "your value and voting power is directly tied to your net worth" are in any way comparable. You and I have zero effective power over them, and always will.
> The 'voting' and 'steering' in a corporation is also completely dependent on money.
It is not, eg. Zuck didn't control Facebook because he was a priori rich, he became rich because he controlled Facebook in a successful way. He gained those shares and that control with his skill and labor (and maybe one symbolic dollar or something).
The unit of power in stock corporations is dollars, while in democracies it is personhood. In the former, one person can acquire multiple units, while in the latter they cannot. There is an obvious difference.
No, a corp is only accountable to their board and the LARGEST shareholder. A single person can control an otherwise publicly traded company. Zuckerberg, for example. And not everyone can afford to spend their earnings owning companies. So what you get with a democracy is that power is spread out by default rather than concentrated in a single element. Default enfranchisement rather than the polar opposite. One at least nods politely at the idea of upward social mobility in passing while the other eschews all pretense as to the status of its party invitation.
Corporations only have any accountability in so far as the law of the nation-state they're incorporated in grants it.
Corporations only exist as a legal construct of other entities. Absent government, they wouldn't be corporations since there'd be no law to create them.
The problem is, when the majority is held by pension funds, ETFs and Blackrock... there isn't much governance in practice, particularly from the low-fee purely passive ETFs. And since government run pension schemes are on their way to the gutter in favor of stonk market private pensions, the share of such dumb passive capital will only grow.
Stock corporation, even if flawed, are accountable to their stock holders at least to an extent; thus your point
> Private companies are accountable to no one
clearly does not hold. Corporations, of course, can also be steered and course-corrected (shareholders meetings).