There's a number of issues with Switch game carts. Longer load times, higher price and sometimes a download along with it eg. Wolfenstein II. eShop games are more expensive in order to match the higher price of the physical cartridges. The Switch's portability aspect makes space a major design factor. Perhaps it would have been better to avoid cartridges altogether and include more than just a tiny 32GB internal memory.
Absolutely not. Eliminating an option is never a good thing, and as a couple of people have already mentioned, you would also eliminate resale value and hurt businesses that offer game rentals and aftermarket sales (Netflix, Redbox, Gamestop, and your local Mom and Pop videogame retailer) if digital was the only distribution method for games. Additionally, Nintendo would never lower the $60.00 standard AAA just because they're saving a few dollars on eliminating the physical cartridge format, they'd just pocket the extra profit.
While downloading digital is usually the most convenient (unless you live in sluggish internet community) way to play games, it also comes at a high price, eliminating the ability to transfer your license for the game to another party for money, trade, or otherwise.
Gamers have been to lazy and not outspoken enough to change how digital distribution works because they're blinded by the "convenience" factor, and publishers are slowly taking away that benefits that we've enjoyed with physical releases. When digital distribution does become standard and purchasing physical games are no longer an option (which I think will take longer than people are speculating) they have to give consumers more benefits with digital distribution:
1) The ability to rent ALL games for a set amount of time. PSN does offer a cloud based (I'm adamantly opposed to cloud based gaming until input lag is equal to an offline experience) service to rent older games, this needs to be expanded to all new releases with the option of not streaming the game in the cloud.
2) The ability to resell and transfer digital game rights. I know companies such as Robot Cache do offer their own digital distribution resale service, but this needs to be adopted as standard across all digital shop platforms.
3) If a rental policy can't be implemented, than there needs to a refund policy similar to what steam currently uses.