but it is significant."
The apis can be rested on the shoulder. The logic behind citing this as a reason for the concavity and rim is as follows. The aspis is heavy and held in a double-grip that does not allow it to be put down easily, so a rim was added to allow it to be rested on the shoulder. There are problems with this logical progression.
The aspis is heavy, but much of the weight is added by the thickest part of the shield, which is the thickened shoulder section near the edge and the off-set rim. Thus the means of carrying the weight is responsible for a good portion of it.
Throughout Greek history we see many heavy shields. Large Mycenaean shields appear to have aided in carrying this weight by the use of a shoulder-strap or telamon. The smaller, but still robust shields of the later Macedonians is also equipped with a shoulder-strap. Were bearing the weight of a heavy shield the only concern, the use of a simple strap makes far more sense than an unique, heavy shoulder rest rim structure. Resting the shield on the shoulder is surely something hoplites did to bear its weight, but this function arose as a consequence of the heavy, offset rim, not as its source.
As an aside there is an excellent reminder of the power of fashion in the design of military equipment. In Italy, magna graecia, we see a type of helmet known as the Italo-corinthian that is designed to look like a corinthian helm worn in this way, but cannot be worn pulled down. There is no functional reason for this, the faux eye-slits surely weaken the structure, but the force of fashion is strong.