Going public is a huge bureaucratic nightmare. Staying public brings on extra costs, efforts, and regulatory requirements... not to mention the public now will judge every decision you make and your company's valuation is as dependent on the whims of the stockholders as any actual business drivers.
While going public does grant benefits, it comes at a price that is not always worth it.
I have no insight into this but for the sake of curiosity and discussion:
I wonder if it has to do with how Stripe leadership is reading the market. There are different opinions I have read that I wonder their thoughts on: some percieve the market is doing great and will do better as we head out of quarantine with these vaccines, some percieve an incoming correction and recession due to some hollistic snapshot of economies internal and international; some speak of incoming devaluation of the dollar. I just wonder if things like these are weighed heavily when thinking of going public, and I wonder if they should or shouldnt be. I know little of economics and markets so I cant say.
Don't worry if they get big enough and don't join the capital markets they will get killed off. It's hard to do real business with a fortune 500 if you aren't listed. Look at SurveyMonkey they ended up relenting.
the gossip I heard was they backed away after crushing the SMB space, because they realized they could take on Enterprise. Stripe is trying to position themselves as the AWS of payments, and it'll take them a couple years to really get a foothold in the enterprise market. then they'll IPO.
While going public does grant benefits, it comes at a price that is not always worth it.