I don't think this is a great idea. Suppose a random piece drops, and its a medium armor with strength, but you are the only one in the group with strength mainstat. You are unquestionably entitled to need on it (assuming you do need the mods), but this system would prevent you from doing so. In addition, in most cases it is the mods that matter, not the orange shell. Whether the armor is heavy or medium is really irrelevant. An example for this: a heavy armor piece with dps mods should clearly go to a mara over a jugg tank. If there is a jugg dps and mara, and both can use the mods equally, it does not make sense to give the piece to the jugg only because the shell happens to be heavy.
Truth. This is why there is such fierce competition over certain Campaign and DG tokens and the rest literally no one wants. Its like when you're min/maxing your Black Hole gear - your entire setup is built out of a whole lot of Boots. (Boots for Mara's at least)
@OP: the gear that is dropping pre 50 is irrelevant don't even bother picking it up. Get 50 get your free gear and then grind to min/maxed DG.