One point at a time....
Merit badges.
Two points to make here.
First of all regarding "badges" reflecting trade achievements - e.g. flying badges, para wings, submariners dolphins. These "badges" serve several purposes. Firstly it allows other people in the military to determine someones specialization at a glance. Secondly, these "badges" are usually earned at the end of very hard training courses. They represent a visual record and obvious reward for great effort and achievement on the part of the individual concerned - they have "earned" their wings, dolphins, etc. They are generally worn with great pride and help to generate "esprit de corps" - something that is probably sadly lacking these days in civilian life.
At the end of the day the military still go to war, fight, and die for their country. Quaint as it might sound, it is still the case that the military do not generally risk life and limb for David Cameron or the Queen, but rather for their friends, colleagues, regiment, Sqn, ship, etc. A strong esprit de corps can be the difference between winning and losing a fight - that's one of the reason for some "badges".
My second point. Some of the "badges" I assume you refer to are rank insignia. The concept here is quite simple. On meeting someone, whether it be in peacetime at an office meeting, or in a firefight in Afghanistan, you instantly know a persons rank, and also their likely responsibility, experience, who is in charge, etc. This also allows for the quaint concept of paying "compliments" to a senior rank.
I'm sure other people can add various comments on the subject of "merit badges", above were my immediate thoughts, and as a two fingered typist, who is being nagged by his wife to do something else, that's as much as I have to say for now...!