How come code to source bash_completion cannot work as it is put inside the
file /etc/profile correctly initialzed/ run
It's needed there and then, if sourcing it being inside the ~/.bashrc file, it's too later and inefficient for a user who always need to or often re-initialize it.
Please show the best way to set up with such demanded
Have you got the "bash-completion" package installed? That's if you are using bash as your shell, if you were using zsh for example you might want zsh-completions. Completions don't work very well without that package, it's separate on Arch based distros unlike in Debian ones where I think it gets installed with Bash by default.