The "loss leader" concept is Business 101, and Groupon was presented to customers as a gallery of loss leaders they can shop.
Actually delivering a good loss leader is hard. Design the offer wrong, and people don't attach properly-- they either don't load up their cart with additional, higher-margin items, or they don't return for future full-price services. I suspect Groupon didn't help-- if they provided consulting, it was probably to steer the merchants to give the store away to make Groupon look compelling regardless of bankrupting the merchant.
Over time, a lot of industries pulled away, either because they personally ran the numbers or simply saw their peers trying it and losing their shirt. The offers eventually retreated to what could survive in the cost structure: stuff like classes (near-zero marginal cost per attendee) rather than food or personal services with significant cost of goods or labour.