"The games are on cartridges.. what year is this?"
Assuming you are referencing optical media: A year in which optical media is actually having a hard time keeping up with cartridges in capacity and size and gets blown away on random read speed. (Possibly raw read speed too, depending on the specs.)
In the PS1/PS2 era, the optical media advantage in size and price per MB was clear. In the PS3 era it was possibly less clear, but still advantage optical media. But that advantage is largely gone now. The only advantage optical media has now is that it is still cheaper to make per MB (or GB if you prefer now), but carts have gotten cheap enough that that isn't necessarily a killer anymore.
Plus as I understand it, very few games even now fill a DVD, let alone fill a Bluray. And the optical media have some very significant disadvantages that are getting worse and worse relative to the rest of the hardware over time, particularly random read latency. Even the PS3 era required a lot of hacking under a lot of game's hoods to arrange the exact order things appeared on the disk to be able to stream in at anything like a reasonable speed, which is why this generation just straight-up requires you to install it to a hard drive (at least sometimes, I don't know if it's every game)... and even the hard drives they can afford to put in consoles at scale are starting to become performance bottlenecks themselves!
Optical media also means you aren't portable, which is a bit of a downer for the Switch.
Assuming you mean "why include anything at all and just let people download to local flash", I imagine it's because Nintendo still wants to sell to people who may not have internet connections that casually download 5GBs. Also, cartridge ROMs are a lot cheaper than flashable media, which is still expensive relative to the size of modern games to put in a console. I've got 512GB of very nice flash in my laptop, but that part alone cost more than the entire Switch. I imagine hitting their price points with enough flash to make it so that you're not constantly deciding which 5 AAA games you can fit on there would be quite difficult. Plus if they do ship out a game console in which the games are constantly "thrashing", Nintendo will actually pay for all the additional downloading that will result. And the end-user result is poor; "hey thanks for inviting us over but three of us need to agonize over which games to delete and then three of use will use your network connection to re-download Splatoon 2, oh dear, look at that, it's gonna take 5 hours" is not what they are looking for.
SD cards are not a perfect answer either; quality varies greatly. I can see why the 3DS has gotten away with it even as a putatively AAA console might not want to trust it entirely. It would help if people didn't buy the cheapest thing they could find with the capacity they want, but they do.