I'm a sysadmin who manages thousands of bare metal machines (A touch less than 10,000 Linux boxes). We have gotten to a point in some areas where you can't linearly scale out the app operations teams by hiring more employees so we started looking at container orchestration systems some time ago (I started working on Mesos about 3 years ago before Kubernetes was any good). As a result, I got to understand the ecosystem and set of tools / methodology fairly well. Kelsey Hightower convinced me to switch from Mesos to Kubernetes in the hallway at the Monitorama conference a few years back. Best possible decision I could have made in hindsight.
Kubernetes can't run all of our applications, but it solves a huge class of problems we were having in other areas. Simply moving from a large set of statically provisioned services to simple service discovery is life changing for a lot of teams. Especially when they're struggling to accurately change 200 configs when a node a critical service was running has a cpu fault and panics + reboots. Could we have done this without kubernetes? Sure, but we wanted to just get the teams thinking about better ways to solve their problems that involved automation vs more manual messing around. Centralized logging? Already have that. Failure of an Auth system? No different than without Kubernetes, you can use sssd to cache LDAP / Kerberos locally. Missing logs? No different than without kubernetes, etc. For us, Kubernetes solves a LOT of our headaches. We can come up with a nice templated "pattern" for continuous delivery of a service and give that template to less technical teams, who find it wonderful. Oh, and we run it bare metal on premise. It wasn't a decision we took lightly, but having used k8s in production for about 9 months, it was the right one for us.