"Zero waste" isn't exactly zero. Even in nature there is a little leakage (like carbon deposits that led to our fossil fuel bonanza). In industry, zero waste is defined as at least 90% diversion from the landfill. More and more cities are establishing zero waste goals. Check out this article that reveals the strategies they use.
Why would cities want to go for zero waste? We are burying millions of dollars of valuable materials. And some of those materials are a real problem for municipal landfills (like lead in old TV screens) which they then have to manage in perpetuity. And there are jobs in recycling. A Circular Economy is the future.