You can still do this on Switch, I played local Mario Kart co-op with my friend on a camping trip a couple years back.

Though there's no Download Play any more. Though I can't say I really miss it all that much. It was practically an upselling/demo feature. I recall playing Mario Kart DS local co-op, and if you didn't have the game you had to play as a Shy Guy. It's not really going to be a fun competition with friends if the host has an advantage.