I'm not sure that in your example that 'for example nurse or doctor' quite fits either - 'imagine I am a nurse or doctor' would be more pleasing but in the twitter generation brevity has replaced accuracy.
It bugs me too, because it should be used to show an example that isn't true, but similar to the correct example. And instead, people use it to give the exact example. I always think they might as well just tell us, then!
I work in health care (think physio, speech therapist, etc) - when the person is really an occupational therapist but wants to keep things vague, is OK. But other contexts just seems odd.
I too think it’s part of a story-telling narrative, a bit like starting with “so” is about setting the scene for the tale that follows.
It’s consciously putting a particular image in the listener’s mind. I can imagine a group of sitcom-writers using it in a brainstorm to quickly conjure up an image in everyone’s heads, a shortcut for “so for example, think of..”.
Here’s my imaginary example: “OK, so we need to establish Phoebe as the hippy one, think flowy dresses. Rachel’s the fashionista, think short skirts and funky haircut. Chandler’s the big dull dud, think boring brown sweater vests.”
So by saying “think” instead of “so for example she/he might wear” in these cases you’ve saved around 21 syllables!