VEMBRACES

[Medicus matt]

We did some training as legionary, from the typical strike I can infer that your sword arm is very exposed.

What's the typical strike? I'd have thought that in close order you'd thrust your gladius into your opponents groin/guts/ribs/face through the gaps in the shield wall without exposing your hand at all.
Surely that's why the legions were so effective? Because they didn't run around waving their swords all over the place like barbarians, viz Vegetius:

They were likewise taught not to cut but to thrust with their swords. For the Romans not only made a jest of those who fought with the edge of that weapon, but always found them an easy conquest. A stroke with the edges, though made with ever so much force, seldom kills, as the vital parts of the body are defended both by the bones and armor. On the contrary, a stab, though it penetrates but two inches, is generally fatal. Besides in the attitude of striking, it is impossible to avoid exposing the right arm and side; but on the other hand, the body is covered while a thrust is given, and the adversary receives the point before he sees the sword. This was the method of fighting principally used by the Romans, and their reason for exercising recruits with arms of such a weight at first was, that when they came to carry the common ones so much lighter, the greater difference might enable them to act with greater security and alacrity in time of action.