I'm not sure I buy any of these discussions, especially the "Long Term Stock Exchange".
In a company, you have a board and you have shareholders. If you don't want the mould of a public company, you create or keep it as a private company. In a private company, you can do any of these employee stock options or buybacks or long term things, much as you can do with a public company, if you wanted to. The board and the shareholders have a similar sort of dynamic in both, but I would say the board of a private company invites less scrutiny, or at least less fully public scrutiny.
So what is the difference between a public company and a private company---in the context of this discussion? The main difference is that in a private company, especially if you didn't set up your shareholders agreement in a friendly way, you can have deadlocks where shareholders can't sell their stock.
This I think is what JPMorgan is targeting, and based on my experience, it's a pretty clever segment of the market to try something, since, as the article and I mention, private companies have inherent difficulties to trade stock (especially if the shareholders are not fond of each other). The stock value of private companies can be undervalued too, and this would mean that JPMorgan would create additional cash out of thin air. Or rather, by analogy magically unlock lost Bitcoin wallets.
Some examples of private companies: Carlsberg, Lidl, Aldi, Deloitte, PWC, IKEA, Koch Industries.
What I find interesting is that this article about private companies was posted after the, ehm, funny LTSE one (seriously, the London Stock Exchange is LSE...) and it would arguably be the closest existing structure where you are not bound by public company expectation, and in theory you could build a rather charitable setup from a private company, much like the LTSE article's prose likes to promise.