Black rim on top of tank. How important is it?

[Delphinus]

The glass can withstand some amount of flex, how much it will see and how much it can withstand will depend on factors like thickness of glass used and height of the aquarium and so on. Bracing will reduce the flex. The black plastic trim however will have way more flex to it than the glass itself. Unless the black plastic itself has a cross brace, it's not doing anything other than maybe preventing someone from getting cut on an unpolished glass edge. If it does have that cross brace though then it is a different matter.