No company could be held privately in perpetuity. Taking ownership away is very different from taxing ownership.
In my model, either company can afford to buy back the stock from the auction thus keeping the company completely private, or then it does not, thus diluting current ownership.
(I personally would expect a tax rate of around 1% p.a in my model. If your company can't buy back 1% pa of its stock without needing to pay any other tax, I am not sure it is a healthy company)
Last, strongly ideologically, in my opinion limited liability is so massive benefit given to the owners by the society that I am not sure there is any reason to even have perpetual private limited companies. Either you grow up to public scrutiny of a publicly traded company or you do not succeed and die trying.
(But just to note, currently I am forced to pay tens of percentage points of my total salary as taxes.)
As for taxes, yes we all pay more. But we do not have our earning power attenuated each year because the government forces us to put ourselves on some incremental slave block.
One of my pet ideas is to stop taxing income/profits of limited liability companies completely. Instead make the the companies issue a certain percentage of their stock to the tax authorities annually. For public companies, Tax authorities just sell the shares in exchange. For private ones, the shares would be auctioned publicly.
Outcomes: - No negative tax cashflows to companies. Ever. - No need for creative tax accounting. Only ones left to fool with accounting are the owners of the companies. - Strong incentive to simplify corporate structures. Any company owned by a company would add to tax burden of the ultimate owners.
(For private companies, it might be nice to allow them to ask to postpone the auctions for e.g. 5 years if they want to keep the control of the company but are short of cash to buy the stock from the auction)