Magnus on 25 September 2015
For the N64 Nintendo was actually developing the 64DD which was meant to be released a year or two after the N64, with carts being only a stopgap solution. For some reason they couldn't get the thing ready in time, so the N64 was stuck with carts. The 64DD used its own magneto-optical media developed by Nintendo partly due to fear of piracy and partly because they didn't have a partner who could offer them CD technology, as the deals with Sony and Philips went sour.
For the Gamecube it was because of the design they made for the console. I don't know why they are so focused on small.
The Wii and Wii U don't have DVD playback purely because Nintendo doesn't want to pay DVD and Blu-ray royalties. At this point, it's not a big deal.
