The Upside to buying media remnants is the cost and exposure. When you purchase remnant space, you're getting drastically discounted prices for major exposure in Print, Outdoor, TV, Radio and Digital. It's not uncommon to pay 85% less for a spot than the rate card cost. People compare it to buying your hotel room or plane ticket at a vast discount, even though the person sitting next to you paid full price. This low cost also means that advertisers with a very limited ad budget can get access to media that would usually be well out of their budget.
The Downside is you also have to have your creative ready to go at a moments notice. That means having your production department and account services ready to move quickly in order to take advantage of any last minute deals.