That's why you always gib players.
Also, Medics do not have infinite syringes, so they can't just toss them out forever and using a syringe takes about 3 seconds - it is not instant. This can be seen in gameplay videos.
I've watched most, if not all the gameplay videos, many times over. I know that there is a short animation while you're
still on the ground, but that doesn't exactly help opposing players because it doesn't show that someone is getting ready to pop up and shoot you in the face with a shotgun as you struggle to repair a robot / plant a bomb / capture a command post / [insert special, time-consuming activity here].
And about the energy pip thing, I know that most skills are limited, but there will be skills to increase the amount of pips you have, yes? And the heavy medic will no doubt have at least 5 or 6 bars, judging from the number on a medium player. And that, my friend, is plenty to capture an objective.