Most of them aren't even directly related to killing. For example the self driving car competitions they have held will eventually revolutionize the way the world transports people and goods.
That project exists to create autonomous military vehicles for use in war zones. Civilian use is a side effect, not a goal.
I'm glad you get a chuckle from the idea that spending more on domestic issues will help with domestic issues. It's pretty self evident. Pointing out that people spend money poorly is simply a red herring and has nothing to do with it. The same hold true for the idea that these issues are too complex to consider funding as a solution. That line of reasoning is why we don't move on fixing so many of these problems. Politicians simply say it's too complex and nothing gets done.
Take the unemployment problem for example. The US has a major problem with failing, old, and crumbling infrastructure. You can have a major impact on both issues by spending federal dollars on repairing that infrastructure while employing people in every state.
I'd say the 13 billion we are spending right now on the new aircraft carrier CVN 78 (Gerald R Ford) would make a significant difference in the lives of Americans if spent domestically. I definitely don't think what this country needs is another aircraft carrier so we can bully other nations and kill their people.
Instead of DARPA which is for military research, how about spending that money on a civilian research foundation. Focus that spending on something like the antibiotic crisis and solve a problem that effects everyone everywhere instead of lining the pockets of the defense contractors who are in the business of ending life.