Yeah, carts would be cool, and it's almost a given on a handheld... but, reallistically speaking, why would they use carts on a home console when equivalent size Blu-ray discs are a lot cheaper?
Xenoblade Chronicles X is like ~22 GB on Wii U. Zelda BotW will surely be bigger or around that. They would need to use a 32GB+ cart to store a game that size. That surely would be more expensive than a double layered Blu-ray, right? Max cart size they've used on 3DS is 4GB... 8 times that to store a game like Zelda BotW sounds a lot to me (unless they use a crazy compression system).
Don't get me wrong, I would love to see carts instead of discs again on a home console, but I see it very complicated.
Well, 32gb flash memory can be had as customer and with related USB periphery at roughly 5$ (Buying in low-key bulk, like 20-100 pieces)
50gb BDs go for roughly 2$ in the same scenario.
Assuming very large wholesale, media cost is probably around 2-3$ for flash memory (cartridge) and 1$ for BD.
Although, there's another matter to consider: BD readers are much costlier than practically-free flash drive connections, to the tune of ~10-15$ to free.
There's also the consideration that a custom port makes piracy that much harder, that not including a BD reader reduces space, weight, noise and power consumption of the console, and has much higher read speeds, meaning you don't need to install the game, meaning you don't need a 1tb drive inside the machine. Well, you still need it for digital purchases, but you can probably get away with a smaller one.
So... there's actually a chance.. if Nin wants a 32gb cartridge. If they want more, around 50-64gb, wholesale flash is probably around 5$, which makes it definitely unfeasible.
Even at 64gb, if they want to push for having their console as light and cheap as possible, it could make sense to bite the bullet on the per-copy cost.