Let's start by assuming that the SEC think that capitalism is a good idea, and that the property rights of owners should be respected. I'm not saying that _I_ think that, or think the converse, but I think it's a reasonable bound for the present conversation.
The CEO, and the company in general, are already accountable to investors (i.e. the collective owners of the company), to exactly the same degree that (s)he'd be accountable after an IPO, modulo only the fact that presumably the CEO's ownership share would decrease. The owners of a private company can require as much or as little transparency or accountability as they choose, with the added benefit that they can require that the transparency only extend to themselves (the owners), and not be made public to the benefit of the company's competition. In constrast, the owners of a public company cannot choose to require less transparency than the SEC demands. So the current owners stand to gain nothing from this additional restriction. In short, whether or not the company (and its owners) benefits from the access to additional capital that hopefully comes with going public, it's hard to understand how any of the other features of going public could possibly be superior to staying private.
I understand why the SEC exists, and without having an opinion of whether the actual SEC actually does their job well, I think that having such an agency promotes the public good, by making investment in public companies safer, and thus in turn giving companies better access to another form of capital, and thus in turn allowing greater economic collaboration between strangers. That's a pretty cool thing! But when the SEC says "Hey, companies that don't need public capital, you should voluntarily put yourselves under our control. It'll help your 'discipline'", I just cannot fathom how that makes sense, except through the cynical lens sarcastically expressed by @fiatmoney.
How can anyone take this argument seriously?
There may be some public good promoted by forcing companies to go public. I don't hear anyone making that argument, though. And besides, what of the property rights of investors?