Skimming over the paper, I think the magic of Homa is in its RPC calls and its short-lived connections. When they're handled at layer 3 and 4, they can provide a significant hint to switches, routers and hosts regarding prioritization and congestion control. If you agree upon the prioritization algorithms as part of the protocol, then both sending and receiving hardware can coordinate much more easily.
If we instead just implemented something like Homa on top of UDP, it would basically mean that the top of the OSI stack would have to somehow inform the lower layers of the stack about these "sessions". You'd also have to hope that 3rd party peers decide to implement the hints in the same way. This would result in much more complexity.