Actually… I have a legitimate question here. The Legend of Zelda: Breath of the Wild was broken on launch for the Wii U, and required a day one patch to play. It’s been stated that people who bought a game from the eShop will retain their ability to download it. But has it been clarified whether people who buy cartridges or discs secondhand will still have access to patches? (The fine article implies yes. So the obvious next question is, when will those capabilities be shut down?)

No, but some of the game's features will stop working. It's not a huge deal for Pokemon because it's primarily a singleplayer game, but that isn't the case for all games. Splatoon, for example, is a primarily online Wii U game that will no longer be playable at all after this shutdown (they had already shut down the servers for this game earlier this year due to a security issue, and took 5 whole months to fix it before bringing them back).

As time goes on, more and more games become reliant on online servers to function, more and more of their functionality is lost once those servers are shut down.