It would also tell the other medics that you are going for that objective. This is important because then the other medics on your team can go revive downed teammates. If you hadn't used the objective wheel, however, you would most likely have 2 or 3 medics going to save the hostage and no one to revive team mates.
You're view on medics are a bit off, medics are always (In most cases) at the primary objectives because that is where the action is, that is where the medic is needed to support his fallen / injured teammates. They are not wandering off to the edge of the map just to revive one player (That will never happen because the player is more likely to tap out and go into next spawnwave) .
Medics will be around the primary escort quest objective, because that is where they are needed, that is where your teammates will die. How the escort objective itself is working is a bit hard to tell because I haven't seen how it works yet.