Why don’t more IPOs do an auction to set the price? Trying to determine the “right” price ahead of time seems like a really bad way to do things.

An auction for IPO price is much easier to manipulate and can lead to much volatility. Pre-allocating to the entities that are not expected to sell quickly or participate in pump-and-dumps (pension funds, etc.) is considered a better long term strategy for the company, as the sister comment says.

Didn't Google solve this with their dutch auction?

Yes. But Google being Google it got top notch planning advice from world class auction experts that Goldman pulled in to advise them on the IPO.

Most companies without such expert advice could step into some pitfalls. Just a guess, I am not an expert, but if my company were doing an IPO I would prefer it not to play financial games to eke out a percent of IPO price and instead focus on long term price stability to become a solid stock. My 2c.

Figma's stock quadripled in price from 33 to whatever it is now. Not saying it's good or bad, just that those gains must have been nice with effort akin to staring spreadsheets a while and babbling in meetings.

What makes an auction easier to manipulate or more volatile than a stock traded on the market?

Likely nothing once the stock is actually trading with some history. But for initial placement wall-street-bets action could be very disruptive.

The company wants to avoid sharp drops after the IPO, as those encourage employees to get out ASAP, which increases the volatility and discourages large, stable investors.

Price discovery is impossible to do except on the market. You can call up everyone you know and ask them, but there are limits to forecasting.

We all knew the Switch 2 MSRP, but we had to wait for launch to see the eBay Buy it Now price.

In this case, the banks are Best Buy. They sold out quickly! Other market players are eBay sellers: the ones that knew what they were doing made a killing selling to consumers.

People like it when an IPO pops. It's a good news story and it makes all the banks who participated happy. If it was priced perfectly it'd get reported as the stock was flat, if it's a bit underpriced then you get headlines as the hot new stock that's taking off

Are headlines really worth billions of dollars?

I think Altman or Musk might think they are. At least they are sometimes.