The problem is that updates are not automatically inserted in the flashcart. All the flashcart does is clone the original one as it was put on sale. Updates are always downloaded by the console and are not stored on the cart.

Let's make a real world example: you go in a store and buy the cart for "disney dreamlight valley" for $40. You actually don't know, but inside the cart there's only a 34,6 MB file that only contains a splashscreen and a popup that says "connect to internet to download the update". It then connects to Nintendo servers to download the 4.61 GB "update" that is the actual game. If you are blocked from Nintendo servers how can you get the update? Your console itself isn't hacked, so you can't just download it from random online sources with a different signature. You can dismiss the popup but then you can only admire your new $40 wallpaper.

This is the "gameplay" of said $40 game if you don't have the possibility of installing updates: