Shouldn't going public on an unrealistic market cap would cause more issues than benefits? Sure, a healthy exit is ok but later pressure to recover the market cap in the short term can cause heavy structural damages inside any org.
I think that's a more complicated explanation than necessary. If their private valuation is higher than their public valuation it means they can raise money more cheaply while private.
The restriction of not being able to liquidate their shares on the public market because of Stripe staying private for an unusually long time (Block (formerly Square), the other double-digit billion-dollar Silicon Valley payments company founded in 2009, went public in 2015). I imagine most Stripe employees that joined in 2019 and earlier expected Stripe to have gone public by now.
That they continue working at Stripe, instead of pursuing other life goals.
Or to phrase parent's point differently: by not IPO'ing, Stripe forfeited the premium public markets would have been willing to pay Stripe employees for their stock.