These objects I'm about to show you almost seem like design school exercises, but they're all actually on the market. First, let's back up a sec to the classic wastebasket, the key part of that word being "basket." Prior to the invention of plastic films and garbage bags, this was where you threw waste. All that was needed was a vessel, and the basket was the most economical way to do this.
Eventually we transitioned to tin and later, pressed steel wastebaskets, as those materials were then abundant and affordable.
Then the garbage bag came around, and the vessel-like nature of the wastebasket was no longer truly necessary, as the bag is now the vessel. The basket or can is there to give the bag something to hang onto. Yet we've largely stuck with enclosed wastebaskets.
UK-based manufacturer AJ Products, which kits out offices, warehouses and workshops, makes wastebaskets that smack of an ID school assignment. Imagine the brief is to re-think the wastebasket or garbage can, and reduce them to only their necessary elements. That's how you'd get AJ's Pedal-operated refuse bag holder with lid:
"This pedal-operated, refuse bag holder can hold any size refuse bag, making it ideal for many different locations from schools and offices to train stations and warehouses. Made from sheet steel with a white, epoxy powder-coated finish, the sack holder is fitted with an elasticated bag cord around the top of the holder to keep the refuse sack securely in place. The lid improves hygiene by keeping waste covered while the pedal operation allows you to deposit rubbish without touching the bin. Use the sack holder with transparent bin bags to improve security."
This wall-mounted version uses even less material, though the lid must be manually opened, which I imagine would be unpopular these days:
This light-duty rolling version doesn't feature a lid at all. I can see it mostly being useful in a light manufacturing environment—say, a sewing facility—where it occasionally needs to be moved a few feet to either side:
And this heavier-duty rolling version with handles and more robust casters would be useful in a shop environment or rolling clean-up situation, like going from desk-to-desk in an office. You've likely seen some version of this in a hotel hallway:
You can see more of AJ Products' offerings here. (I liked looking around in their Warehouse & Workshop section the most.)