That's a great question, and one I've definitely asked myself when facing an oversized city-issued trash can! The short answer is: you *can*, but it often doesn't work well.
A standard 13-gallon kitchen bag is designed for a small, indoor bin. When you try to stretch it over the wide mouth of a large, wheeled urban can—which often holds 32 gallons or more—the bag usually won't fit snugly around the rim. It will sink to the bottom, leaving the sides of the can unprotected. This means liquids and messes go directly into the can itself, leading to stains and awful smells.
Even if you get it in, a small bag filled in a large can becomes very heavy and is much more likely to tear when you try to lift it out. It's a recipe for a messy spill on the sidewalk.
A much better solution is to use a bag actually sized for the can. Look for "large trash can liners" or "32-gallon+ bags" at the store. They are stronger and have drawstrings or flaps that secure over the rim. If you must use a standard bag, consider double-bagging for strength, or use a smaller secondary bin inside the large can to hold the bag in place. It saves you from cleanup headaches later!