Why is the “cursed” snake still with us?

The snake itself was not cursed to destruction in Genesis 3, but rather to crawl on the ground. The curse against the snake was an ignominious change in its form resulting in the snake becoming least among all creatures, as we see in Genesis 3:14:

Gen. 3:14  The Lord God said to the serpent,
“Because you have done this,
Cursed are you more than all cattle,
And more than every beast of the field;
On your belly you will go,
And dust you will eat
All the days of your life;

God cursed the snake "more than all other cattle." In other words, the curse on the snake was that it would be stigmatized among all animals of the earth. So the snake was required to enter the Ark so that it could continue to serve as a memorial to the fall of man. Forevermore, the world may look upon the form of the snake as it moves on its belly and remembers the mistake Adam made to bring the world into sin. 

In fact, since sin continues to exist in the Kingdom to come, the snake will continue to go along on its belly the Kingdom for the same reason:

Is. 65:25 “The wolf and the lamb will graze together, and the lion will eat straw like the ox; and dust will be the serpent’s food. They will do no evil or harm in all My holy mountain,” says the Lord.