I think that the shield-wall can be used in several different ways. I say this more as a historical fan than a fan of The Last Kingdom (because let's be honest, the shield-wall in Vikings was absolute garbage and wouldn't protect them at all). The way the shield-wall in The Last Kingdom worked was that there were three tiers or ranks that they placed. The first rank would kneel and have their shields at the base of the wall, which would allow them to strike the enemy's lower body, like the legs and the knees. The second rank would stack on top of the base. This is the area where the soldiers would be able to attack the chest and neck of the enemy, so they're level with each other. The third rank would allow the men to be protected from above, keeping the enemy from efficiently striking the men in the wall with axes or swords from a downward swing. They generally didn't try and attack due to them having to hold the shield above the head.
A lot of people say, "Oh, well the shield-wall wouldn't work that way because the men needed a lot of training to be able to keep that formation." Well, that's true. However, the whole reason for the shield-wall historically was to keep the enemy in position so there could be a flanking maneuver. The men inside of the shield-wall wouldn't want the wall to break at all, because as soon as it does, it's nearly impossible to reform a line. So, with that, they would train with this formation and adapt to whatever weapons they used with it. The Greeks used the dory and pikes or essentially any long spear to keep the enemy from getting near their shield-wall. Thus, the Greek Phalanx.
Saxons mainly used spears for medium-distance combat, but they also used short-hand weapons like swords (for the wealthy) and axes. In the show, many of them used the seax (yes, Saxons used the seax, too). The seax is practically a short-sword, which would be very useful inside of a shield wall, and not very difficult to use in the first two ranks. Spears would be useful for the initial moments in the engagement, but when there are a bunch of sweaty, hairy Danes striking at you and trying to stab or hack into the small holes in the wall, a short-sword would be much easier to use.
In conclusion, yes, I believe that in history, shield-walls could very well have been used this way. After all, one long line of enemies only a few shields thick wouldn't prove very well if they're past your spears and hacking your legs. I'd love to hear what others have to say, I just love to think of possibilities like this.