The laws changed for IPOs. It used to be when the total investors got over 500, including employees holding shares, that would trigger a company to need to go public. It was changed some time ago (not sure if JOBS act or what) to be much higher, like 2000 investors and excludes employees.

This means companies stay private and keep getting private capital/investments (the flip side being private equity in the pre-IPO company) and typically an IPO is really existing shareholders realizing their investment.

So Amazon, Microsoft were forced to go public much earlier, then had their growth. Anthropic has already had growth, Claude AI is well known at this point, and after IPO there may not be as much growth after. In fact, the stock might go down because they have to report their full financials.