My impression is that the Trisolarans allowed the droplet to be inspected specifically to taunt humanity. When Ding Yi and the fleet representatives discover the incredible material properties of the droplet, they realize that it could only be made with advances in fundamental physics, which (given the sophon lock) humanity cannot possibly match:
"What force would allow that?"
"There's only one option: strong interaction." ...
The droplet wasn't fragile like a tear. Entirely the opposite: Its strength was a hundred times greater than the sturdiest material in the solar system. All known substances were as fragile as paper by comparison. It could pass through the Earth like a bullet through cheese, without even the slightest harm to its surface.
"Then... what's it here for?" the lieutenant colonel blurted out.
"Who knows? Maybe it is really just a messenger. But it's here to give humanity a different message," Ding Yi said, turning his gaze away from the droplet.
"If I destroy you, what business is it of yours?"
In other words: Despite humanity's technological advances following the Great Ravine, the weapons technology of the Trisolarans could draw on advances in fundamental physics that humanity could not obtain, and so humanity's fleet could not hope to beat the Trisolaran fleet in a space battle. The Trisolarans wanted humanity to know this. The reason why they sent this message is unclear, but it's possible that it was simply to foment chaos on Earth (which it did remarkably well.)