I work for another large supermarket and used to be responsible for dealing with the markdowns and waste, and I'm trying to think of what we'd have done if we ran out of labels. There'd be no easy/efficient way of getting them through the checkout without any labels to show the checkout operator that they need to override the price manually instead of just scanning the reduced label. We wouldn't be able to change the price on the system, because that'd cause ALL of that particular product to go through at the reduced price, not just the short coded ones. I expect some one would have got a bollocking when the waste bill was seen for that day.
The store HAS to account for all the stock going in and out of the doors, anything not accounted for causes shrinkage and affects the stocktake (and stock ordering), so just giving it away isn't as easy as it sounds.
All waste in my store is documented - and as a previous poster pointed out, a lot of it is down to customers dumping chilled and frozen products in unrefrigerated areas, or products that can't be frozen and resold into the freezers, or damaging packaging (letting their babies/toddlers hold food items which they'd then bite/put fingers through, having their children sit in the trollies and squashing things, which they then dump at checkout or go and swap when they notice it, or by trying something from a multipack and then purchasing a whole, unopened pack, or just plain old theft by consumption) In fact I'd say in our store this accounted for about two thirds of fresh waste.
All our waste is scanned for documentation, bagged up according to whether it's bakery, raw meat or cooked fresh goods and then sent off for recycling.
As for marking the food down - our system takes off approx 10% at the first markdown, more if there's an excess of one product. At second markdown there is slightly more taken off - there is significantly less to do at this point and even less at the third markdown, very little to markdown to 25p at 7pm. So even though some people refuse to buy it at first markdown, considerably more will. It's worked in our store and for our company overall for a few years.
There is huge pressure to reduce waste in supermarkets, and as far as I've experienced they do take it very seriously. They can't win either way, because for every person who wants to see the waste go free to customers, there's two more who'd quite happily sue for anything they find out of date.