The US Government isn't brave or cowardly.
Some of there actions are brave. Others cowardly.
No. They really aren't fighting a war.
They are using the military as an international extrajudicial hit squad.
Call it a "war" to rationalize it is like rolling tanks down main street to wage war on shoplifters. After all, we can't simply send the police... they might get injured, how can we take that risk? We should use every advantage we have, all the time... right?)
The "brave" alternative is sending troops in to get killed. That's not a solution, then you just get more people killed.
There are a lot of options between "drone strike at wedding" and "boots on the ground invasion"; lets not frame the question as a binary choice.
And if you don't like policy, you don't frame it in terms of how effective we are at fighting
How we engage is as important as policy. We could use ICBMs, with nuclear warheads too, without loss of American life. That doesn't make it a sensible choice.
Drone strikes at weddings aren't sensible either.