Hello @lf-araujo, the compositor is MIT licensed and there shouldn't be a problem putting something together with your distro's package management.
However, the actual packaging for the compositor should be handled on a per-distro basis and should remain separate from the steam client. This PPA or the documentation here looks like a good starting point for packaging on Ubuntu.
Your system information
Please describe your issue in as much detail as possible:
This is a suggestion for improvement.
Thank you for your software, it works very well under Ubuntu. My suggestion is that together with the SteamOS, Valve could permit the steam-for-linux to be shipped with SteamOS's compositor and window manager. A login option in Lightdm or GDM could be added to log into BigPicture+SteamOS compositor so the user would be able to have a more or less similar experience as a SteamOS in their laptops or desktops without the overhead of an underlying desktop environment.
All the best,
lf