The thing is, for the Xbox One and PS4 games get installed to the hard drive BECAUSE disk-based media isn't fast enough for playback anymore. That necessitates the need for a larger hard drive and storage management, something Nintendo would rather avoid. Cartridges are a better solution for Nintendo. Whether or not other systems follow suit remains to be seen. Sony and Microsoft have always used disk-based consoles (and Sony even had a disk-based handheld) so they have no experience with cartridges. It's up to them to see if they will be a better idea - if they ever come out with anything after the PS Neo and Scorpio.
Sony did/does with the Vita. Of course most PS4 games are too big to make cartridges feasible as the sole hard copy storage method for reasonable manufacturing costs.
The Switch will probably need a lot of expanded storage to download addon content for the games to keep up with the graphic quality of the other consoles, but since many games are Nintendo platform specific they usually don't have to compete in areas like FPS where players admire the graphics almost as much as the total package.