Given that AP ticket holders must travel on their booked train, I'd say they are more in need of a reservation than the holder of a walk-up ticket.
Unless the AP ticket holder fancies standing up for their journey, they will want a guaranteed seat on that train. Their allocated seat may not be their preferred choice, and on an empty train they may move, but they have a guaranteed seat. On busy trains they might not want to sit by a pillar, but I bet they'd rather sit next to a pillar than stand in the vestibule for three hours.
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If you are able bodied and able to fight your way on to a train first, you won't see the need for reservations.
Try travelling with a young child or a grandparent, or someone with mobility issues, and you'll soon see why reservations are a good idea.
The Euston Stampede should be enough to convince you reservations are a good thing.