>... why would they go public?Your comments left out the #1 overriding reason for the IPO: It's to raise money for growth. The IPO is a means to an end and not the end goal itself.
A company can try to _raise money_ (let's say $1 billion) a few ways:
+ bank loan -- an old 100-year old company like Boeing with a track record can get a bank loan. A startup with no collateral cannot.
+ corporate debt -- again, Boeing has a track record of revenue and profits and can issue commercial paper that ratings agencies can assign a risk (AAA, B, etc) that bondholders will buy. Boeing's bonds rated AA pay 8%. A startup's attempt to issue debt notes would be classified as "junk bonds" and they'd have to pay crazy interest (30%?) to attract bondholders to take on that risk of not getting paid back. Also, if the startup has no revenue/profits, they don't have money to pay the regular interest payments.
+ divest, sell some assets -- again, a company like Boeing can sell off some piece of themselves they don't need. Boeing recently sold off their cybersecurity business for millions. A startup doesn't have any subsidiaries, manufacturing plants, or unneeded technology patents they can sell.
+ equity offering a.k.a. IPO -- sell shares of the company to the public. As a plus, this can raise more money that the previous methods. This option is open to startups.
Sure, it's possible for startups to "raise money" by bootstrapping and let profits fund the growth. However, the point of the IPO is to raise money exponentially faster than bootstrapping.
So, companies don't just go public purely for the sake of "going public". They want to raise money and the other options for doing so are not available to them. If the startup doesn't need to raise money, they don't need an IPO.
All that being said, a cynical person can still say that VC's and founders can still push for an IPO more for "cashing out" instead of "raising money". It's possible to have that hidden agenda, but that's not the majority of cases. When a company starts the process of an IPO, the underwriter (Goldman Sachs, Merrill Lynch, etc) and the company management have to go on a "road show" to convince potential buyers (pension funds, etc) that they have growth ideas that will make wise use of that money. Having a pre-IPO Powerpoint slide that says, "we want to your money because the founders and VCs want liquidity to cash out" isn't going to convince people.
So, "why would founders want the pressure and stress of shareholders?" ... it's because they wanted the shareholders' money. Same thing as wondering why Joe Blow "wants the stress of a boss?" ... because Joe wants a paycheck... it's just that the "boss" came with that salary.