It has actually been said that naturally-produced testosterone is not what everyone thinks it to be. In fact, the most mellow, peaceful men out there are full of naturally-produced testosterone. The testosterone problems come from either a lack of testosterone or an abundance of artificial testosterone. The stereotypical steroid-head out there, who injects the stuff, is full of artificial testosterone, which the male body does not really handle all that well. Sure, you can build some really nice biceps, but it is not the real stuff and the rest of the body, including the brain, gets thrown off by this lack of the natural stuff. These guys are nuts, because the body turns off its own production of natural testosterone, and everything is thrown out of kilter. The body balances hormones quite well in most people, and to alter this is very problematic.
All the problems above - war, religious strife, domestic violence, thievery, those are not testosterone. Don't attack what makes males male. War is want, greed. So is religious strife. Domestic violence is when men are not taught how to be men by responsible male figures, which should be fathers, but sometimes take the shape of brothers, grandfathers, uncles, step-fathers, a good next-door neighbor, etc. Responsible men are taught that the women in their lifes are to be PROTECTED. That is our job and role. Thieves are also lacking morals. Again, lack of a strong male role model. We must be taught to EARN, not to TAKE. Attack bad fathers who do not take responsibility for their half of raising a child. Attack greed and irresponsibilty. A child is both your pride and responsibility. And half you.
With that, a decrease in testosterone would actually contribute to the world's problems. Testosterone is not the problem. Testosterone is the solution. Let boys be boys. When they get to be boys and work out some of the issues of growing up, they become good men. Boys beat each other up. Boys go fishing in the pond. Boys get dirty. Boys build forts. Boys go dirt biking, heavy emphasis on the dirt. Boys who are precluded from these things get screwed up and do wacky things. They cannot progress to be good men. Boys have dreams though, like flying the space shuttle, or becoming a businessman, or teaching, or flying a fighter jet. After all ladies, you may have sons one day, do you want their father to be a role-model who brings them camping in the remote wilderness, teaches them what every airplane is at the airport and shows them stuff or makes them sit around and watch TV?
I discussed this with a public health nurse, a male nurse at that, who was very well informed on the topic of male testosterone, which also ties to male health issues, something us guys don't do a very good job of taking care of sometimes. The last thing any guy on this Earth wants to talk about is something like testicular cancer, yet a ~1mm tumor is fatal.