If we were in a field though would they be just... done? The only thing I could see winning based on what was shown in the manga would be like compact catapults or the cannon, yet speed-wise I’m pretty sure that number of box formations would only lose like one or two before marching within their effective range.
Moving in formation is difficult, especially when you're carrying a 10kg/22lbs shield over your head and keeping it close as possible to defend against arrows. Combine that with the mixed armor, longs spears (not quite pikes) and crossbows and ammo, you're moving at a snails pace. There's been reenactments of the Roman testudo that had the reenactors moving about 1-2km/h or 0.6mph, after training for several months.
As far as real life examples go, the Romans didn't use testudo for field battles unless they were facing heavy arrow fire, because the formation can easily get outflanked. I also remember that it was primarily used in sieges for the legionnaires to get close enough to breach defensive positions.
even without formation the enemy army was more well armored, better trained, better morale and in higher numbers, there is no reason why they should not still be winning out of formation...
The purpose of the formation was to counter the cavalry charge and horse archers. Having the formation broken means being vulnerable to both, and Aegir says as much in Chp99, pg 17
The Magrad infantry's armor isn't better than Aegir's infantry, and "weaker" than his heavy cavalry. Both infantries were wearing a plate cuirass over mail, the difference being the helmet for Magrad having better coverage than the kettlehelmet Aegir's infantry were wearing. The Magrad heavy cavalry was also wearing brigandine, which is less protective than the full plate that Aegir's heavy cav were wearing.
The Magrad infantry did have good training...for fighting in the box formation. Once they were no longer in that formation, it's hard to say if they were better trained on an individual level than Aegir's troops.
Better morale is highly debatable; both cavalry were already scattered, one box formation was crushed and routed, and the supposed allies they were helping were already routed earlier in the battle. So Magrad went from a combined force of 15,000 to say 7,000 effective versus Aegir's force of 10,000.
Again, at this point of the battle Magrad didn't have overall higher numbers. Their heavy infantry might've outnumbered Aegir's infantry, but Aegir's cavalry nearly matches the surviving heavy infantry regiments.
TL;DR the box/testudo/shield formation was the one advantage the enemy had, specifically to hard counter arrow volleys and Aegir's yolo cavalry charges.
