As for an example of where you'd want multi-round, you could imagine a scenario where you have a feature A which gets bugfixed by the introduction of feature B, and you don't want to expose that you support A unless you first negotiate B. Or if you can negotiate B you should never expose A, but for old nodes you'll still do it if B is unknown to them. An example of this would be (were it not already out without a feature negotiation existing) WTXID/TXID relay.
The SYNC primitve simply codifies what order messages should be in and when you're done for a phase of negotiation offering something. It can be done without, but then you have to be more careful to broadcast in the correct order and it's not clear when/if you should wait for more time before responding.
Actually we already have service bits (which are sadly limited) which allow negotiation of non bilateral feature support, so this would supercede that.