OP is likely making assumptions on obsolete knowledge. Tech moves really fast which means the knowledge we gained last week might no longer be relevant. Here is an article showing it is perfectly acceptable to deploy Postgres in Kubernetes:
The great majority of Kubernetes experts I have met use a managed service and have not been exposed to the internals or the control plane back end. An abstracted version of Kubernetes that works well for most use cases but makes it more difficult to solve some of the problems listed in this thread.
Most folks dont really know Kubernetes. They know how to deploy X application using X abstraction (Helm, Operators, CD tooling) to some worker node in a public cloud using public sources and thats basically it. It's no wonder they cannot solve some of the common problems because they didnt really deploy the apps. They filled out a form and pushed a button.
High-performance database engines take complete control of their resources, I/O, and scheduling, completely bypassing the OS kernel. Linux is explicitly designed to allow this. This architecture enables integer factor improvements in throughput on the same hardware, which is why you would design your software this way. Older, slower database engine designs (e.g. Postgres) don't take explicit control of resources in this way and will work reasonably well in containers.
The original Linux container design was never intended with this type of software in mind, and tacitly reduces the control a process has over its resources. Invariants required for performance are violated, and therefore performance suffers relative to bare metal (or conditionally VMs). The v2 container implementation, which isn't widely available yet, recognizes these problems and attempts to remedy some of these poor behaviors of the v1 container implementation.
If your database does not assume strict control of its underlying hardware resources then this does not affect you. However, this kind of strict resource control is idiomatic in all the highest performing databases architectures, to great effect, so it is the most performant databases that are most adversely affected by containerization.
FWIW, virtual machines used to have similar terrible performance for high-performance databases for similar reasons. Now there are mechanisms for the database to effectively bypass the VM similar to the kernel, and the loss of performance is minimal. Container environments typically don't offer similar bypass mechanisms.