Grocery stores _absolutely_ supported the bag bans, though they weren't the initial groups asking for them. Similar to how the cigarette companies liked the TV ad bans--if nobody could advertise on TV than the playing field would be level and their profits all went up from decreased costs.
Some of them supported them because they were pressured into it. Grocery bans of bags and payment etc. are a PITA for customers. No business in it's right mind would force that on their customer unless they were required to. Passing the cost on to their customer is not an issue. Supporting laws requiring payment etc. are cost benefit analysis. Is it worth fighting the bad PR etc or go along. But obviously they wouldn't have provided the bags in the first place if it was not a competitive benefit to them.