A two stage trigger is best for making deliberate, accurate shots with. You can stage your breathing with the trigger. Breath out and acquire sight picture as you take up the slack, half your lungs out at the wall...hold your breath/verify target, break the shot.
In a military application, I'm to understand It's a bit of a target verification type thing. It gives the shooter that brief moment of "do I want to". If that is BS, and I suspect it might be, a two stage trigger is certainly safer than the alternative when grouped together in a trench or on horse by the thousands (two stage triggers were widely adopted during late 19th century conflicts). Either way, it is a deliberate design.
Without the stage, if you're not really, really familiar with the rifle, you won't know when the sear will release. Where are you with your breathing, sight picture, etc., etc., when the gun discharges?
Two stage aside, the only more accurate trigger is either a hair trigger (really fvcking dangerous), or a set trigger which at least lets you know when things are about to get, really fvcking dangerous!