Instead of exclaiming "Eureka!", would it not make more sense for Archimedas to facepalm instead, thinking "How the hell did no one else think of this before?"?

No, it was a remarkable insight. Like lots of physics, even today most people aren’t aware of it.

That’s the tragedy of science in ancient Greece. No emojis, and no memes.

“Eureka!” makes a better quote.

It must not have been obvious if he had to figure it out.

The story makes it seem that what Archimedes discovered is trivial, but what Archimedes’ figured out, known as Archimedes principle, is fairly sophisticated and not quite so obvious. For example, consider a boat floating in water. The volume of the boat below the surface displaces an equal volume of water, and the weight of that volume of water equals the weight of the whole boat. The reason that dense objects sink in the water is that the weight of the water that they displace is less than the weight of the object.