This sort of already exists. Many companies take on university students to intern for 3 months over the summer, and offer full-time return offers to seniors. At least in the US Bay Area, this is substantially more common than offering internships to full-time employees. Mainly for the reason people mention: 1-3 months is a huge time investment for what amounts to an extended (albeit paid) interview, when they can interview somewhere else and get a full-time offer with no uncertainty.

Google also offers associates or something similar to that. But it's for much longer, 6 months or a year.