By "elected government" you mean Hamas, which has sworn to annhilate Israel? How do you negotiate with someone sworn to your annihilation?
Israel has suffered years of terrorist attacks and bombings and was able to tamp that down only through action that won it condemnation. How much more of that would you like?
Saying that it is a Hamas government is misleading. Hamas is the majority but the government includes Fatah, smaller parties, and independents. It has men and women, Muslims and Christians, and peace activists. It is not like Hamas is running the whole show.
Israel is dedicated to the destruction of Palestine, so everyone would be starting on the same page in negotiations.
Israel is in the uncomfortable position of having to attack civilians to stay in power. This attack on civilians brings more opposition and more attacks on civilians. Israel is on this downward spiral.