Another reason I'd like to have the Bravery not decrease on first encounter (where you run away)
It doesn't. It's designed this way for this purpose and for high level characters traveling in low level regions.
You'd think that you'd lose more bravery % points just by running @ first site, then by standing and fighting & figuring out you're going to die and then running...
The first sighting gives you an option of assessing the situation. If you decide that you are low on health, unprepared for the fight, or the fight takes more resources than it's worth you can get out while you are ahead.
It would really mess up the statistic to have every encounter count against you. Especially since at high levels you don't have the time to play with monsters when you are trying to get from place to place.