It's one thing for Google etc to invest billions in cash and cloud services[1] into Anthropic with the understanding that money will be used for engineering and growth.
It's quite different for any buyer to come in and spend $4B on the secondary market for nothing but shares, with none of that money going to Anthropic.
There is a large appetite for exposure to the big AI companies, so maybe the demand is there. But it's not as simple as selling a large stock holding on the public market.
[1] https://www.axios.com/2023/10/30/google-invests-2-billion-an...
There are tons of big private equity funds and several trillion-dollar fund managers for which buying a 10% stake of a privately held 30 billion dollar startup would just be a question of some paperwork.