Interestingly enough, this doesn't just apply to puppetry, but also animation as well. Nick Park, the creator of the lovable plasticine duo Wallace & Gromit, and other animators at Aardman Animation, share the exact same mindset, that it's the imperfections that give the characters their warmth and realness - hence why whenever you watch any of the Wallace & Gromit films (or, really, any of Aardman's work), you often see the fingerprints and thumbprints on the characters. For Nick Park, it also goes beyond just a sense of warmth for the characters, but he also feels this is a way of showing a little bit of the artist themselves in their art. I don't even know if the layperson would even understand that, but I definitely think I do: as long as I've been watching and observing anything Muppets for almost all of my life, I can kind of see a little bit of Don Sahlin in the puppets he's built, or Kermit Love, or Caroly Wilcox, or Ed Christie.
To get a better understanding of what I mean, here's a collection of WALLACE & GROMIT'S CRACKING CONTRAPTIONS shorts, as well as a behind-the-scenes featurette, in which you can hear Nick Park and his fellow Aardman artists discuss this very thing (starting at the 20:14 mark):