That's an interesting and practical question about our everyday urban environment. From my observation, it really depends on the specific design and location of the bin. In many modern cities, you'll find a mix of both.
In high-traffic downtown areas, parks, and near transit hubs, I've noticed that more and more public bins have lids that are permanently attached via hinges or integrated designs. These lids often have a small opening or a flap that you push your trash through. The goal here is clearly to prevent litter from scattering in the wind, to reduce odors, and to discourage animals from getting in. They seem quite secure; you'd need tools to remove them.
However, I have definitely come across older models or simpler designs in quieter neighborhoods where the lid is just a separate piece of plastic or metal that sits on top. These can be lifted off completely with no effort. Sometimes they're even left off, leaning against the bin, especially if it's overfull.
The trend seems to be moving toward attached, more secure lids. It's a simple design choice with big implications: attached lids help keep the area cleaner and are more vandal-resistant. Removable lids, while easier for maintenance crews to empty, often lead to messier surroundings. So, to answer your question directly: many are attached, but you can still find ones that aren't. The design largely depends on the city's priorities for cleanliness, cost, and durability in that specific spot.