Thus my caveat "we know of".

However, while it would be quite possible for a victor to erase written mention of a rival, it is harder to erase beyond all archaeological recovery the signs of a major city that's been stable and populated for a thousand years or more. For instance, if we look at Jericho, which was inhabited earlier than Ur was, we don't see archaeological evidence of it becoming a major city until much later than Ur (see link and link).

If there was a city large enough and long lived enough, around before Ur, that passed onto Ur the bundle of things like writing and hierarchy that we known Ur passed onto others, then I'm unaware of it, and the evidence has been surprisingly thoroughly erased (which isn't impossible, but neither is it a certainty that such a thing happened).

See also the comment about Uruk. There were a number of cities in Sumer close together that would have swapped ideas. But the things said about calories and types of grain apply to all of them.