I still don't get what you mean (or exactly what you mean when you say "installing"), Postgres can be a simple executable on OSX and Windows and on linux it is usually "installed" because it needs to setup a data directory, user/group, config directory and so on.
There is nothing about linux that makes postgres more or less portable than on windows or osx, and I'd be interested if you have any examples of postgres being used in a non-packaged way (outside of development tools like postgresapp.com).
Besides that, one of the strengths of most linux distros is that they provide a centralized way to install/upgrade packages like apt/yum/dnf/pacman and don't have to rely on third party tools like homebrew.
Yes, the OS doesn't impose any opinion. It's just a matter of what application developers do, and the developers of Linux applications tend to write code that doesn't require installing. As an example, there's Postgres :)