That analogy doesn't work. You already downloaded the games, they will play just fine. You just can no longer download the games you deleted, just as you can't purchase a record at most stores if it was lost/damaged/stolen.
The Wii store is a piece of shit and I have tons of problems with it, but it's also been up for over a decade at this point. At some point, your ability to download purchased games was going to end.
A physical game, movie, CD, etc.... it not limited to a particular device and it not bound to me either. This means when one Wii dies (and they do die) I can simply use my physical Wii game on another device (or I can give it away, trade it, etc...). If my CD player dies, I can play my CD in another device. You say ten years, well I have things I've owned for over 20 years, original N64 games and the like, and they can play just fine in any N64 console. They're not bound in some way to my original console, and a physical item doesn't exist only so long as I preserve space on a hard drive for it.
That aside, this doesn't fully explain the downsides of owning something digitally. I try my best to put very little into digital content I have, but I still have enough to know what's going on. For instance there are people who have movies on Vudu/Ultraviolet/iTunes that literally vanish. As in they had them in their library and they're gone now do to licensing issues. "Owning" digital content is really nothing more than a rental. Now you might say yes but you can download them and keep them forever, but c'mon. No one is going to download hundreds of movies or games just in case they vanish from a service and even then they're at the mercy of a storage device and DRM limitations.
Services have gone offline, bans in the past have prevented people from accessing accounts and downloading their digital content (Microsoft for example), and due to DRM, (GOG being an exception), you can't really backup this stuff either. So, you're trapped in a position where your digital content will rely entirely on the life your a particular device and the nuances of the DRM. Your storage dies and so does your collection.
It would take my house burning down to lose all my games, but all it takes is one Wii dying and you'll lose all your digital Wii games. That really sucks.