The khopesh was a solution to the limitations of bronze as a sword material.
Bronze swords can't be too long because they break. Bronze is more brittle and less flexible than iron. For this reason, bronze swords were used only as secondary weapons. The Greek xyphos was only used when the doris (spear) broke and some hoplites never trained with it.
The khopesh is a sickle sword. The curved blade has a very forward point of balance, making it similar to an axe (in fact, it evolved from axes).
It's an excellent hacking weapon, which makes it very useful to attack limbs not protected by armor or even break shields. It wasn't used "to get around shields" but through them, and neither "to puncture" because it is difficult to change direction between cuts, the point is almost blunt and backwards and the sword is too short for good lunges.
When swords began to be made with iron/steel, the extreme shape of the khopesh became less valuable. There are still "hacking" swords, like the Greek kopis (with a name so similar) and later the shotel or the scimitar, swords that favor the cut instead of the thrust. The form we usually call "machete" (falchion, etc.) has been popular in all history.
So, basically, ancient and medieval armies used the khopesh, but because it was made from steel, it didn't have its exact shape.