For a long time most historians assumed that shields were thick, tough, 30-pound, metal reinforced oak tabletop style pieces of kit that was held tightly to the body to take incoming blows.
A survey of viking and medieval shields shows that they were thin, light and very flimsy to the modern observer who expects weapons and gear to be twice as big and five times as heavy.
We have a significant gap in our understanding of pre-gunpowder warfare. Theories differ wildly.
Fighting in some kind of close formation was known since early antiquity and everything since was a variation on the theme, more armour, less armour, longer spears or the inclusion of missile troops etc.
From early medieval sources come words like Skjaldborg and Scildweall and while we have some descriptions, we are ultimately unsure to what degree the shieldwall has to be interpreted. Are they just a figure of speech designed to emphasize the fighting toughness of warriors in some kind of formation or are they meant to represent troops cleverly overlapping shields to give them immunity to enemy fire ? It's hard to tell, even harder to give a definite answer.
Clearly they understood that fighting in formation against anything but panicking monks and villagers was sound tactics. And if they were slow on the update the first defeat would probably have resulted in major changes to the official operations manual.
The key issue here is the flimsy nature of the shields which according to the author couldn't have resisted for long to intense fighting.
There is a side issue that has yet to be resolved. Was the shieldwall a static, defensive formation or were they capable of moving and marching per the Greek Phalanx.
For a long time it was assumed they lacked the sophistication to form an advancing shieldwall, as if the inhabitants of a Greek poleis somehow had access to uber-ninja level skills that completely escaped the Scandinavians.
Marching in a group is not evident, but it's not hard, tests have shown you can get random people to march in reasonable formation and keep it while on the move. Sure it's not paradeground precision, but is that really the point ?
One of the issues is that viking shields are not that fundamentally weaker than say Roman shields. The Greeks did beef up their shields, but many other armies used even simpler wicker or hide shields.
There is some evidence based on later medieval manuals that shields were not simply held to the body as just another layer of armour, they were used actively, projected forward, partially to absorb blows that would otherwise hit the body, but also to hinder and control the opponent's weapon, while creating opportunities to strike the enemy.
Again people have no problem seeing Romans use their shield proactively in combat, but doubts are raised as soon as a viking is suggested, invoking images of somebody foaming at the mouth, wielding an axe the size of New Hampshire.
Shields were light because an axe the size of New Hampshire looks good in Fantasy art, but sadly due to a gap in legislation, people are not condemned to wield such an axe every day for an hour to teach them the error of their ways.
Weapons are designed to be as light and handy as possible.
So they came up with something that was light enough to use actively for a period of combat without exhausting you and giving as much protection as possible. In the end it's a tradeoff.
The fact that the shield is not the equivalent of a reinforced bank vault door is probably more indicative that a light shield is better than none and doesn't preclude some kind of formation.
In reference to something like Stamford Bridge the use of armour become highly important in the later viking age when they fought trained troops on a regular basis. A man wearing a helmet and mail byrnie was probably adequately protected against arrows and the shield would add additional protection to the face in addition to catching the arrow and slowing it down enough to prevent it from doing any real damage.
They might not have gone all out testudo, but it's hard to rule out that they didn't form up and fought defensively especially against missile troops.