Yes, I think large battles were much less frequent occurences than small encounters if warfare was more endemic and more of a requirement if warfare was sporadic. A round
shield is very well suited to beat up someone without exposing yourself, whether in line or not. Line combat can be a special warfare situation and a lot might depend on the regulation of activity. Front ranks can act in a more "skirmishing" manner and retreat to the safety of their common line with more mutual support. This concept can be developed into line combat with very solid lines and correspondingly arm-strapped or at least temporary(Scutum) ground-posed shields of tight ranks. Development of equipment and concepts will mutually depend upon each other with modifications of existing templates before switching to something new at the exclusion of prior design features. I wasn't referring to the Sutton Hoe shield, but to the Bayeux Tapestry Huscarls. These straps can help to use many weapons with two hands, not only Dane axes.
Scythian/Sarmatian ornaments seem to reflect a similar idea of strapping shields in different manner for utilizing the bow or the spear/xyston, while switching to a center grip mode if using axes or the akinakes, but the source and concept make it no recognizable example for infantry line combat.