IPOs aren't the magical moment that they were in decades past. You get to answer to a bunch of retirement fund managers and "the market", meaning less-savvy retail investors. You have to open up your books.
It seems like Anthropic, OpenAI, etc. are doing an IPO because they are literally out of other options. Older IPOs like Facebook felt different, like the hard part had been done, and they just had to scale. There's a difference in selling something because you want to, versus selling something because you have to. Facebook was just relying on the idea that they were a platform that more people would inevitably sign up for. For the most part, they did. It seemed obvious. They likely could have continued on by simply operating privately, but the IPO gave them capital to dominate the market.
Anthropic and other hyperscalers cannot continue on privately. They're facing a systemic shortage of capital to achieve their goals. They need the infrastructure, and there's not enough capacity to make enough for all of these companies to survive.