No it is not. Israel got its own people out of the Gaza strip years ago and hasn't let them back in since. Israel supplies Gaza with water and electricity because Hamas prefers to spend its resources on building tunnel networks and rockets instead of power stations and water treatment works. It is also militarily superior and has nuclear weapons. If they actually decided to "annihilate" Gaza it would be a smoking pile of glass tomorrow, as the military capability is there.
> an enemy that lives next door and is indistinguishable from the citizenry
The IDF wear uniforms and are easily identifiable.
> Doing nothing is not an option
They have lots of options, including making peace with Israel. Step 1 would be to replace the government committed to its destruction, with one that is willing to talk instead of launch rockets. But the Palestinians seem to support the existing strategy.