The way the scenario is constructed the humans certainly don't have much of another choice. You could say that it's only that way because the author has chosen to frame it in a way that makes military power seem like the only option, or you could make the case that he wrote it that way because it's intense and interesting.
I do kind of wish there was a little more to the science side of the story, with more focus being put on research into finding other ways to kill the titans, but we did get a little of that and may get more eventually. Seems like with as dangerous up close and as easy to manipulate as the titans are some sort of chemical weapon would be the safest, fastest way to kill them. I think it was established that they don't have to breathe, but they seem to most of the time anyway. They're probably immune to all forms of poison because that's more narratively interesting. Titans are OP. :derp: