If there are cases (like this) where a single-message compromise is a big deal, and WhatsApp cares about these cases, then the simplest solution would be for WhatsApp to add a preference in the client to switch on—as the article describes—a "blocking mode" for re-key notifications, where retransmissions aren't allowed by default.
t1: Server sends message (1) to Client B
t2: Client B fails to decode message (1) due to an outdated key. Sends failure notification to Server
t3: Server sends rekey notification to Client A
t4: (usually <400ms or >1 second) Client A sends rekeyed message (1') to Server for Client B
For t4, if the Server notices the response from Client A came faster than a user could ever have seen and responded to a notification, it now knows Client A is more susceptible to a MitM attack. If, on the other hand, Client A takes an appreciable amount of time to send the rekeyed message (say, 1 second or more) then we know that either there was a network latency, or the user had to respond to a rekey notification before the message was resent. We should be more careful about launching a MitM attack on this class of user.
So, without changing the actual _actions_ that the Server sees, but just the pattern of the timing of those actions, we're still leaking important information.
Note: all numbers completely made up.
I was more thinking along the lines of discharging rekeyed messages and not showing the message at all to security conscious receivers. Whether this is behavior is good, I can not say, UX tests could give more insights.
And, presuming you are seeing reply-messages from your peer and having a back-and-forth conversation, I don't think it's actually possible for those reply-messages to not implicitly also be ACKs of your own sent messages—the Axolotl ratchet underlying the protocol ensures that (I think. Crypto people chime in?)
So, yeah, you can probably get a retransmitted transcript of one person talking into a void without seeing any delivery ticks in response. You can't really get a conversation.