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).
Which seems to just devolve to "the lizards listen to whoever/whatever has money" at the high levels where the number of voters is very high.
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.
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).
Suffrage*. Not personhood.
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.
By moving the locus of control, whether it be considered the ceo or shareholders, so far from the actual business and implementing mandates based on whatever the current fancy is and meaningless targets of growth on such a giant scale you get the same sort of excesses.
The current system is marked by irrationality and uninformed and ill considered decision making. With smaller organizations and actual business competition they would be held to account by their competitors or just by running out of money before something catastrophic for the greater economy happened.
Large monopolistic mega-corporations do tend to have the same issues that one would see in the old 20th century planned economies like the Soviet Union.
It is much easier to exit from or steer a private org. For example, it is very possible to run a company which caters to 10 percent of a consumer base by providing niche products which may be slightly more expensive. Those 10 percent will simply consume less of some other good. It is very difficult to do an analogous thing at the state level, because we generally don't get individual "ticket books" which we can "spend" on more of one state service vs. another. The democratic model is that you first get 50+ percent support and then your coalition decides how resources are allocated for almost everyone.
In some metrics (such as GDP), yes. And in other metrics (such as wealth inequality and health care), the answer is less clear-cut.