It’s getting less common because it looks cleaner and functions better to have the divider flush with the sides. My sink is flat on top and it’s better because I can set what I’m washing out of the sink. It does get scratched up over time though.

Cheap sinks have the rim they are describing. Expensive sinks usually have a low or no divider. It’s the mid teir that is going flush on top for some reason. It’s a completely useless feature IMO that makes the sink less useful.