The businesses that Groupon works well for have a) unused capacity to service additional marginal customers, and b) good retention/ongoing business once people try them. Good examples: gyms, salons, masseuses, adventure sports, skydiving, concerts, travel packages, overstock goods, etc. Bad examples: popular, crowded restaurants. Unfortunately, people eat out a lot more than anything else, so a lot of people bought Groupons for businesses whose business model didn't match Groupon's value proposition.
This was not well understood in 2012 (well, maybe it was to leaders of Groupon/Living Social/etc that had the numbers) and so the market size was not clear. But everyone knew that the returns would go to the biggest player, hence the intense competition for funding, advertising, customers, and merchants.
I suspect that Groupon's competitive landscape is one reason why Uber has been so aggressive in fundraising and expanding - to win at lower cost than having to battle every every market, and correctly size fundraising to the actual market.
It's basically the same as getting coupons in the mail, but with a lower cost of distribution and a channel that people actually pay attention to.
I suspect Living Social's main problem is that it's a me-too service that doesn't offer much of an advantage over Groupon. Google ended their Offers a year or two ago; also a me-too effort, and I think Amazon Local also shut down.
In the end I decided it wasn't worth the effort trying to build a startup that required hours of our time to convince/train each customer for a meager (<$100 monthly) amount. Way too much overhead.
It's interesting how one's perspective on something differs, one sees it as "cheap" while another sees it as "thrifty". Related to upbringing, perhaps? I love it when I can get two $60 meals for one $60 price.
Secondly, and admittedly on a much more anecdotal note, it seems that these customers are prone to acting entitled and complaining loudly about things that are non-issues compared to the regular clientele. Most people who don't like Thai food simply don't go to Thai restaurants. But there's a pretty decent Thai place near my house that tried Groupon, and got a handful of really bad Yelp reviews from people who seriously seemed to just hate Thai food. A couple of them explicitly mentioned Groupon, and the owner told me that she believes that all of those reviews were Grouponers (and the deal didn't restrict what they could buy, so they got the same food as everyone else). Their complaints had nothing to do about the specifics of the restaurant (which has almost universally good reviews). This serves no one. The diners get a meal they didn't like. The restaurant takes a ratings hit. And Yelp users see artifically low ratings for a good restaurant. If I'm looking for a Thai restaurant, I don't care what people who dislike Thai food think -- I already know they'll hate it.
Groupon and LivingSocial's value-add is allowing a small business to gain distribution relatively on the cheap compared to other methods.