However realistically k8s is in heavy deployment in a wide variety of industries including public sector, financial services, retail, technology ... and it's clear that this kind of concern is not the primary consideration.
There were banks in the UK (Monzo) deploying k8s almost 3 years ago (https://monzo.com/blog/2016/09/19/building-a-modern-bank-bac...)
Monzo, on the other hand, was default-dead, so betting the farm on a relatively unproven technology perhaps wasn't risking as much. Nobody talks about the startups that used unproven tech and sank.
Also k8s is far from only used in tech companies. the UK home office (not exactly a startup) were giving talks about their use of k8s in 2016 https://www.phpconference.co.uk/videos/2016/kubernetes-home-...
Whether or not something is a smart choice to use in mission-critical production applications doesn't depend on the number of big banks or big tech companies that use the technology.
At the end of the day, Kubernetes is a tool that will change
very rapidly over the next 5 years. I could see k8s being a decent choice to use in a tech project that you expect to actively maintain and improve for the next 5+ years, AND if you (and your developers) are willing to invest time (potentially a lot of time) every year keeping up to speed with how k8s evolves through every version release. That's the primary risk in using something like k8s.
The last decade has been dominated by rapid adoption of technologies that were under heavy development at the time, from Ruby on Rails, to Node.JS to Golang to Rust.
The simple reality of modern IT is that companies are unwilling to wait until a technology has stabalized before making use of it.
Personally I'd rather they did, but my opinion has little weight in that regard.
Good example is the recent offer for 147 million people to get 125 dollars out of a pool of 31 million ( Equifax )
As an industry IT is simply shamefully shoddy