Going off the other reply, I wonder if a highly-active secondary market means that companies can raise series [A-Z]+ rounds effectively forever, where each "round" just refers to a giant purchase of shares under strict company supervision. Is this the new game for startups?
I can't speak for the specific case of Stripe, but it's fairly common for private companies to have a "tender offer" in which employees have the opportunity to sell some portion of their equity. This is often done in conjunction with a new investment round.
There's a newish term for this: RLO, Recurring Liquidity Opportunity. These are tender offers at some recurring interval. Even some companies that have a shorter lifespan (say 7 years) offer this.
Having been through an IPO before, it was good for employee liquidity, but bad for the culture and long-term success of the company.