The term “microcopy” has been floating around for a while, so I definitely didn’t coin that word. I’m just a fan of good microcopy :)
If you’re looking for examples where cute or clever copy can be inappropriate, this site has a bunch: http://cruelestoptouts.tumblr.com
I think it really depends on your audience, your product, and your brand. Cute or clever copy isn’t appropriate everywhere, like if you’re working on a government site or a health site. Straightforward microcopy tends to be a safer, simpler, and more scalable choice. But I personally like it when I see companies trying new things with their microcopy.