What is the failure mode the recipients have here?
Frequently developers who implement these manage to do two bad things. First they introduced a lot of complex code which rarely triggers except in disaster, and so whose bugs tend to survive. And second, they manage to convince themselves that they have accomplished the impossible, and make reliability promises that other developers unwisely believe. Exactly how unreliable most systems were and how much the documentation couldn't be trusted was underappreciated until https://jepsen.io/ came along and started proving how bad most distributed software was.
Now it may seem bizarrely unlikely that you'll ever see this kind of situation. But failures often start from network congestion due to a packet storm. And the failures lead to chatty Byzantine fault tolerance protocols adding significant traffic. This causes cascading failures. And so a small, simple outage can escalate into a series of outages as ever more confused servers continue overwhelming the network with their futile attempts to discover what is supposed to be true. So complex combinations of failures occur together more often than most of us would expect.
What determines which failure mode you get is whether the machine will failover to a machine that retries uncertain messages (giving you "at least once"), or it doesn't (giving you "at most once").
But, you say, why can't we have it failover to a machine that asks recipients what they have got and goes from there? Well we can, but the recipients don't know what messages are in the network still on their way to them.
But, you say, why not have the recipients disregard those inbound messages once they know about the replacement machine? Well you can do that, but now the *recipients* become machines whose job is to ensure the deduplication. And now *they* become the machine with a bad failure mode.
But, you say, does this not reduce the odds of failures? Why yes, it does. Which is why people do things like this. And there has to come a point where we accept SOME failure rate.
The alternative, well, read The Saddest Moment at https://scholar.harvard.edu/files/mickens/files/thesaddestmo... to see where madness leads.