The internship should be paid, but at a low rate (not what people expect to get paid after three years of experience).
I've written a couple of blog posts on the topic:
The reality is the designers need experience in real world situations and the best way to do this is work with someone more senior to look over their work. I've had people apply where I work at that were expecting to get a job right out of school. Unless they do something as a side project or intern, they don't have enough work to show design thinking.
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