Sparky! by Jenny Offill and illustrated by Chris Appelhans is another picture book about a child wanting a pet and having to pick a strange one because of strict parental rules. She's told to pick a pet that doesn't need to be walked, bathed, or fed. So she picks a sloth who comes in a box.
Sparky the sloth's introduction reminds me a bit of Baymax's, except that Baymax is energetic and graceful compared to Sparky.
Sparky's by no means the first funny sloth. Sloth's basically hang from trees, eat leaves, sleep a lot and move slowly enough that their fur turns green from algae.
In children's programming there's Snook of the PBS show It's a Big Big World who is lively for a sloth but talks a bit like a Berkeley hippie.
From Japan there's Sloth who lives in Polar Bear's garden, in Polar Bear Café. Like Sparky, he sometimes gets carried around by the woman who works at the cafe.
And now, of course there are the DMV sloths from Zootopia. Long story short, sloths are funny, endearing, and memorable.