Aside from the fact that 98abaile pointed, Linux is not some miracle OS descended from heavens itself, to save mankind from the root evil of the world!
Mac,Linux,Sun,Windows,DOS, all have C compilers.. and thats essentially all you need to create a game.
That brings me to game programming, I dunno if you ever looked into it.
But its not user friendly!!
Its not drag'n'drop create a story and voilà we have a game!
And if you tell me RPG maker II, you deserve to be shot.
Other thing, look PS2 for example, even if you put linux with it with the official LInux kit, do you think 32MB of memory are enough for you to do heavy things? like rendering a CG?
Plus there are better tools then linux for that matter, the SDKs. Tools made expecially for that purpose of creating a game for a certain console.. not linux that is a general tool just like windows.
And for developing you really need a good computer.
But back to the concept of your idea its flawed for the simple reason.
While Console have the downfall of being un-upgradeable they have one thing any programer love! Standards!! All have the SAME hardware, the SAME drivers, the SAME engines..
So if I make a game, and that game work on one console it WILL work on any console.
Now look at PC games, how many don't work because, either, the driver is incorrectly, don't have necessary stuff, conflict with other softwares.
Console is all about user friendlyness, plug in the outlet, plug in the tv, put the cd in, and PLAY!
There is no drive updating, opening it up, upgrading parts!
Lastly the main problem with homebrewing is.. piracy!
If you can burn a game that works on any console, you can COPY a game that will work on any console.
There is virtually no way now for you to diferenciate a licencied game from a copied game from or homebrew game.*I thought for a while here, and with all ideas I came up to diferenciate them, I aways came with one method to bypass that*
Homebrew have special burner > just use the same burner to copy
Original have special tag checking online > block console internet access
Checksum > BIOS HACK..
Just look at the current market, we got all kinds of modchips and stuff to bypass all kinds of protections.
Making a opensource = licence to piracy on current world!
If you want to create games, use the SDKS that you have on your computer.
If you want to create games for a console, get a job at some company!
"Chile is a thin and tall country"