In a few videos on YouTube and in a few topics I read people briefly mention that they want to get rid of Supervised installs? Is it true or I misunderstood something? If it is true, how do they know that? Is there any official statement with explanations?
A “supervised install” (your text) is different from “supervisor” (your title).
The supervisor is a container that does various things, it’s not going anywhere.
A supervised install on the other hand is an installation method that the developers begrudgingly allow as long as some very strict conditions are followed. Judging by the uproar last time there was an attempt to depreciate it, it’s not going anywhere either.
Only the founder of the Home Assistant project can definitely answer that question. However, based on past events, it seems unlikely it will be deprecated in the future.
Here’s the community’s response to the first (and only) time there was an attempt to eliminate support for Home Assistant Supervised installation.
The ultimate decision was a compromise and official support for Home Assistant Supervised installation was limited to just one distribution of Linux (Debian) and not for any other. The decision was officially documented in ADR-0014.