It's not impossible at all. If your inbound is on time it's an easy connection in fact. If your inbound is late, of course that's a problem, but the computer only knows what it is told.

To your more general point, the auto-rebook is computer generated and does not always spit out the ideal solution. You were smart to be proactive and look for something better. (Of course, that something better may not have been available earlier when you were initially rebooked or when you talked to the first agent. The non-stop may have only become available due to someone else missing their connection. Availability changed rapidly during IRROPS).