Where have our Eagles gone?

[Titvs Statilivs Castvs]

The "stylized" images on the coins, I think is more likely a result of the difficulty in ingraving a 0.5 cm. image on an iron die.

I'm not sure what you're implying. That maybe aquilae didn't look the way they are depicted on coins? (The Romans seem to have been able to depict other items recognisably, e.g. the Colosseum on coins of Titus, or the Column on coins of Trajan. Why not an aquila?)

Two more examples of the eagle in flight:

The eagles are recognizable, the Colosseum and the Column as well. But can you see every stone of the Colosseum? Can you see, on a coin, every depiction on the Column? They are, imho, also "stylized", just like the eagles. I don't see why the Romans would make their eagles unrefined/undetailed if they are the pride of the legion, even having a genius.