At its core Groupon is mainly just a different way of offering coupons or sales and in getting the word out on them. Most comments I've seen here one could easily apply to the always hot button topic in business of offering coupons. Theres no shortage of businesses that aren't a fan of coupons.... but there's also no shortage of coupon books, coupon mailers, discount cards making the rounds so there is something to them for the right business. Those coupons (or any business having a temporary sale), like Groupons, are generally not offering a permanently devalued product so much as being clear about a limited time offer of a business' choosing. When a business puts out a coupon, puts on a sale (or presumably a Groupon) they aren't typically doing it with the narrow focus of getting rich off of that one short term offer on that specific product so much as using it as part of an overall strategy to promote their business. Most certainly a promotional strategy that works for one business doesn't necessary work for another business and its product or service and this method of promotion wouldn't be for everyone.
As a point of interest I found the link to the Pita Pita Groupon that expired (its below). 66 reviews, 4 1/2 out of 5 stars on average. Customers loved it, and I know that a lot of businesses love what customers love

(so long as they see the numbers adding up in their overall promotional strategy for their business). You can read the comments, including replies from the business itself. Not a lot there that I'd describe as "terrible for business"
https://www.groupon.com/deals/the-pita-pit-3-29250161?nlp=&CID=CA&utm_source=groupon_transaction_succeeded&utm_medium=email&sid=groupon_transaction_succeeded_20170630&eh=b675647ee24e6edd66094ebcbe64350825509c31558e715a5d1a47a3dc2dfad9&date=20173006&sender=rm&s=body&c=link&d=deal-url
The main issue I can see and really the only strong argument I could see that separates it from the perpetual debate about couponing is that Groupon is ultimately the one taking payments and then they will be charging for that service. From a usability standpoint for the customer thats its strength but its also something a business will want to learn the ins and outs of after signing up and before posting/determining an offer that works for them. I haven’t seen a comment yet in this thread from someone with experience trying it from the business side. Would love to see someone give it a try and be in a position to give first hand feedback (or see first hand feedback from one of the very very few that have tried to date locally).