How did the Danes & Saxons manage to integrate a two handed long weapon like Dane/English Longaxe with the shield wall formation ? Logically when two densely packed shieldwalls meet in battle, stabbing/thrusting/jabbing attacks & weapons like short swords or spears should predominate. A two handed long hafted weapon that requires a bit of swing space seems to be rather unfeasible in the jostling melee, not to mention it leaves the wielder unshielded & thus, open to aforementioned stabs/jabs.
The two-handed longaxe was the province of the housecarls, professional warriors who served in the household guard of thanes and kings alike. Thus, they weren’t the most common weapon on the battlefield, but rather the sign and tool of office of an elite even within the warrior caste::
In combat, the axe was continuously (and unpredictably) swung to create a deadly zone around the axeman, and when that axe hit, it could easily hit with enough force to split a shield open or knock a man onto his back or cut through a spear or knock a sword out of someone’s hand - which made the thrusting/jabbing combat you’re talking about an extremely dicey proposition if the axeman was fast enough to avoid getting stuck.
Thus, the housecarls seemed to function in two ways: first, on the offensive, they would open up holes in the enemy shield-wall for other soldiers to exploit. Remember, the longaxe’s haft could be as long as six feet, making it a forerunner of the polearm, which gave the user a good deal of reach into the enemy line, and the axe’s blade was bearded, allowing the wielder to hook over the lip of shields and drag them down, opening up the shield wall:
On the defensive, the housecarl was there to disrupt the enemy shield-wall, either by opening up holes in their defense or by creating zones that soldiers naturally shied away from.
In either case, the housecarls seemed to function as skirmishers, stepping in front of the shield-wall to contest the area in between. When we look at the Bayeux Tapestry, for example, we see images of housecarls wielding only the longaxe standing between a Saxon shield-wall and the oncoming Normans (which shows you how insanely brave these guys were):