Come to think of it, though, I'm a little surprised that nobody tried to bring back that kind of warfare? Surely someone somewhere had the will, time, and resources to do this?
Standing armies like the Roman empire where kind of rare in the early middle ages. The class that could afford to train extensively in combat was the knightly class, and like many culture the elite favored cavalry.
Another factor that even in the late Roman age tactics were moving away from the massive emphasis on infantry. Roman legions had significantly increased the portion of cavalry and skirmishers. Finally I believe the glory days of the Roman infantry was long before the advent of heavy cavalry.
The Roman writer Cassius Dio gives and account of a defeat of Roman legions that showed a great weakness of the formations when faced by Parthian knights and horse archers
"For if the legionaries decided to lock shields for the purpose of avoiding the arrows by the closeness of their array, the knights were upon them with a rush, striking down some, and at least scattering the others; and if they extended their ranks to avoid this, they would be struck with the arrows."
I can see how similar tactics could be used by medieval knights to disrupt such a formation. Though they would probably have foot archers which would change things a good deal.
Finally the classic Square scutum disappeared itself from Roman usage in the 3rd Century replaced by the Clipeus. So it could be that it was believed the shield was obsolete.
