Can bird strikes be dealt with by throttling down engines to idle?
A goose can easily be flying at 40mph and a commercial jet will be landing at about 150mph, giving a closing speed of about 190mph (305km/h). That means that, to spot a goose with 10s warning, you would need to spot it when it's more than half a mile away.

Not only would you have to spot that tiny speck of a goose half a mile away during the busiest phase of the whole flight, but you'd also have to immediately work out whether the tiny speck was even coming towards you. If it was, you'd have to estimate whether it would even hit the plane.

Then, supposing you'd immediately and accurately recognized the danger to your plane from that tiny speck, you'd have to immediately reduce power to the engines, while being very careful not to hit the ground the bad way.

In short, regardless of how much better the outcome of a bird hitting an idling engine would be than one hitting an engine under power, it's just not feasible to try to power down the engines. Once you take into account the false alarms, which would vastly outnumber the actual bird strikes, trying to power down the engines would probably be far more dangerous than just hitting the bird.