It's actually even worse than that: In more than one aviation accident multiple alarms and alerts actually served to confuse the pilots as to what's going on, causing them to not perform the action that would have saved the flight.
Information overload in the cockpit is a very real thing, particularly in an already task-saturated time like the landing approach. It's entirely unclear that adding yet another alert chime requiring the pilot's attention would help anything.
Yeah I definitely agree with this concern. Rather than an alarm it could be part of the landing checklist. The person not flying would say, "Check approach on <whatever runway cleared>", the person flying would check the display and respond "Confirm approach on <whatever>".
Information overload in the cockpit is a very real thing, particularly in an already task-saturated time like the landing approach. It's entirely unclear that adding yet another alert chime requiring the pilot's attention would help anything.