It’s usually risky to fly one itinerary on separate tickets. That’s because when you’re on one ticket, if you face a flight delay or cancellation the airline responsible for the irregularity has to get you to your final destination. But if you’re on separate tickets they usually don’t — they just have to get you as far as the end of the ticket you’re flying them on.
But it’s not always a risk if you know about this American Airlines policy.