That's a great and practical question! It really gets to the heart of how our city infrastructure works on a daily basis. The short answer is: it depends entirely on the specific design and purpose of the trash can.
Most standard, fixed public trash bins you see on sidewalks and in parks are not designed to be moved when full. They are typically anchored to the ground or are very heavy-duty to prevent theft and vandalism. When these are full, sanitation workers use specialized collection trucks with mechanical arms to lift and empty them directly into the truck's hopper. The bin itself doesn't need to move.
However, for larger capacity containers used by businesses, in public spaces for events, or in certain municipal systems, mobility is key. This is where wheels become essential. You'll often see large, rectangular dumpsters or heavy-duty round bins with built-in wheels and a lid. These are designed to be rolled to a collection point when full or to be easily hooked and lifted by a truck. The wheels are usually large and robust to handle the weight over curbs and uneven surfaces.
So, in summary: Small, fixed public bins? No wheels, not meant to be moved by people. Larger, high-volume containers for centralized collection? Almost always have wheels for practical mobility. The design choice ultimately balances capacity, security, and the logistics of the waste collection system.