Take this simple shield variant.
Here, two angled spikes at the bottom of the shield dig into the ground if the soldier rests the shield but slide along if he advances. Mostly he would carry it in the standard manner ... but ... he has the option of using the ground as a strong ally. For instance, he could rest a bit while the enemy pushed mightily to no effect then push forward when the enemy wore himself out pushing against the ground. Very simple, very effective and ... not used (to the best of my knowledge).
The hook and ring design was well within their capabilities. Here, you hook one shield into the other and make an impenetrable advancing wall. Perhaps in a staged battle, one could attach a pole to each shield and the enemy swords couldn't touch the soldiers pushing it.
This yields new battle strategies like,
Why such styles were not employed baffles me. If you know of any instance where something like the former was used let me know. I'd be interested to find out if it worked as well as I suspect it would have.