Why did Moshe have to make a Copper snake. Wouldn't it be simpler if the snakes went away? (or acted as they were before the plague)
In Likutie Torah, Parshas Chukas(61d-62b), this question is asked. The answer provided is Hashem creates nothing inherently evil,for example lets say Atheism what could possibly be good with that? the answer when someone comes for help and or charity you dont say G-d will help you, no you take it into your own hands.This point is illustrated with the copper snake there is a good Spritual source to ALL things.Moshe was telling them look upwards at the Snake look for its positive spiritual source from Hashem and recognize that the punishment was for the overall good of Klal Yisroel and when Hashem sees that you recognize this then you will be healed. (this is very much my adaption of the idea,feel free to argue if this is the intended meaning of the answer!!)
I am going to add a more extensive answer trying to hit on all the underlying points of the question.First I will address Why A snake was needed to cure Klal Yisroel? The Maharal in Gur Aryeh answers that it was all about looking upwards that meaning prayer.When somthing like a snake bites a person the person becomes fearful of it. This way when you see the snake up there, and you have just been bitten by the very same thing your prayers will be alot more focused and hence Hashem will answer your Prayers.(very practical) He then explains why copper or נחשת: He explains the fact that נחש and נחשת are similar names has a significance since names indicate the essence of a thing, the נחשת heals the נחש because of their similarity.(not so practical).
The Ramban has a whole different approach. He says when Hashem does a miracle he does a miracle within a miracle. He explains this based on the Medical Science of his day that normally when you look at the thing that made you ill you will aggravate the symptoms,and make you worse off. Here Hashem showing them even though normally looking at the snake should make you worse, here I am going to make it, make you better.Another Miracle within miracle was the story of the bitter waters where a bitter tree was thrown into the bitter water and the water was sweetened again normally adding bitter to bitter makes more bitter but here a double miracle happened.[Just a note on this point today's medical science definitely does not concur with that of the Ramban's when you add an acid to a base it neutralizes-hence bitter and bitter is explained]
For the super mystically inclined;The CHIDAH in his Sefer "CHADRIE BETEN" says The reason snakes of נחשת where used is because the original snake was responsible for the early deaths of the children of נח until שת.Hence the cure was נחשת.
I recently gave a Devar Torah on this very question, and suggested that the purpose of using a snake (which had caused them significant pain and fear) was that Bnei Yisrael had to build up some courage to "face their fears". Any time the nation had a problem with something, they would immediately come running back to Moshe to cry or complain, and often suggest running away from their problems. Before they entered Israel, they had to learn how to take care of things themselves; G-d wouldn't always continue to take care of their every need. That being the case, rather than stop the plague altogether, Hashem created a situation in which they had to learn to face their fears, which would serve them well as they moved towards Israel...