We are digital librarians. Among us are represented the various reasons to keep data -- legal requirements, competitive requirements, uncertainty of permanence of cloud services, distaste for transmitting your data externally (e.g. government or corporate espionage), cultural and familial archivists, internet collapse preppers, and people who do it themselves so they're sure it's done right. Everyone has their reasons for curating the data they have decided to keep (either forever or For A Damn Long Time (tm) ). Along the way we have sought out like-minded individuals to exchange strategies, war stories, and cautionary tales of failures.
This doesn't answer your question: Is pirating an option for you? You might be able to grab them more easily that way
My understanding is that original Xbox (and other consoles) need to be modded in order to run discs that aren't original. If you're going through the trouble, you could add a bigger hard drive and just load the games into there
Yes, optical drives can just "go bad" while sitting. Even if not the laser, many of the mechanical parts can age and fail.
There is no "set it and forget it" medium in existence. Multiple copies, in multiple locations and if possible on different media types.
Original Xbox? Why worry bout optical drives just put large HDD in it and load all the games on that then keep HDD backup.