2. Disc or drive will eventually fail
Most consoles distribute their games from a physical disc or cartridge, and those discs will eventually scratch or degrade to the point that they become unreadable. Cartridges are better at this, but they have a tendency to produce errors are they age. As mentioned above, you have very little choices when the game goes out of print.
Current generation consoles use optical drives (DVD or Bluray), and these will eventually need repair. Just like games, eventually replacement drives will not be available, and you will either have to repair it yourself or modify your console to use a standard PC drive.
I had a classic Xbox that would no longer read discs, and I had to open it up to change the focus and strength of the laser in order to make it readable again. This component will eventually fail, which is why all of my games have been copied to a hard drive.
If you modify your console to play backups, then you can either have a playable backup copy of your game, or have an electronic copy on a hard drive, so that you can keep playing your game.
3. Privacy concerns
Most people don’t know that retailers automatically register the serial number with the console manufacturer at the moment of purchase. If your console breaks, there’s really no lying about the warranty period. Most companies have a 1-year warranty that starts at the time of purchase, not the time when you opened it. If you do your Christmas shopping in early September, and your “new” Wii console breaks next November, then you’re SOL. It’s true that many companies will so a “no-charge-non-warranty” repair, but for accounting purposes they’re doing a non-warranty repair.
The bedrock of the previous paragraph is that game companies already know more about the console than you think. If you register your console with the company, or even purchase any games through the console’s online store, then they’ve tied the console to your name. This can be really helpful to find information if you have a legitimate claim. For example, if you purchase a lot of systems and games from them, they know this and will be more willing to work with you if you have a problem.
Most people don’t like the idea of others knowing too much information. If you’re of those that wants to go “off the grid” then don’t use their online stores or register your product.