Say you have two fleets of spaceships on the opposite ends of the solar system, both having plans A and B for attack. They want to surprise the enemy by being unpredictable so despite the enemy knowing about the two plans, if you decide randomly which fleet does which you'd still have an advantage. Maybe one fleet is larger so they could focus forces where they need to be if they knew the plan ahead of time.
But if you choose randomly by default you could have both fleets do plan A, which wouldn't work. But if one measures the entangled pair they both get a mutually exclusive random result and thus can make an unpredictable plan work without a pre-set decision of who does what.
A weird far fetched example to be sure, but I'd imagine cryptography nerds could find a matching case for some kind of encryption or whatever.
Need someone to make it a bit more accessible though…
That may not be very helpful for a battle plan, but if there was concerns about enemy infiltration, the entanglement could be intentionally used early, resulting in neither ship knowing what the other is doing, although the ship that read on time wouldn't know they didn't know.
Your use case fails to take advantage of the fact that the quantum states collapse at the time of reading.