Before you start bashing the Western Allied leaders for the 'idiotic' demand of unconditional surrender, consider their point of view.
First, Germany had started two world wars in 25 years (yes, I'm very well aware that the 'guilt' for starting the WWI is a controversial question, but I'm presenting here the prevailing western allied view of during the WWII). The negotiated peace that ended the WWI did not prevent Germany from rearming and starting another world war. (Again, I'm aware of the argument that a more lenient peace after the WWI could have prevented the WWII, but that's not the issue here).
Second, Germany was ruled by a goverment whose brutality was unheard of before (with the exception of the Soviet Union). All signs pointed that the overwhelming majority of the German people supported this goverment at least passively.
The western allied leaders didn't want to repeat the mistakes in their opinion were committed in ending the WWI. Thus, for them, demanding unconditional surrender was perfectly logical. Unconditional surrender was seen the only way to ensure there would be no more German aggression. IMO all other arguments contain unhealthy amount of hind-sight.
Did it prolong the war and cause more casualties? Certainly. But it was not the job of the western leaders to worry about German losses, quite the contary. And the Allied losses caused by the prolonged war were seen worth the cost of ensuring peaceful Europe.
Now, if only the Americans would have been less naive towards the Soviet Union, but again, that's another issue.