Halberds and similar weapons could be used for both thrusting and striking depending on the situation. However you are correct that swinging these weapons in a dense formation could be difficult at times, which is partly why they became overshadowed by the much longer pike. On open ground, it was generally accepted that halberders couldn't go toe to toe against a push of pike, but they were still considered more useful on broken ground or in less organized fighting.

Typically a pike square involving halberders might look something like this (the "B"s represent Bills and Halberds). Though sometimes a number of halberders would be mixed in with the arquebusiers outside the formation in order to back them up while skirmishing in the flank or forlorne hope. When the time for a push of pike came the armored pikemen in front would be doing most of the actual pushing, while the halberds in the center of the square were mainly just their to add mass. Once the enemy formation started to lose cohesion however, the halberds could break out of the square in order to exploit, pursue, and execute the enemy. The early Spanish Tercios were known for using sword and shield men in a similar manner.

In theory, the halberders in the center of the formation would also be able to more effectively defend the battalion's colors and officers and allow for an orderly retreat if the formation lost cohesion and the pikemen began to rout. However, some writers noted that that typically when the pikemen in front began to lose heart they would back up into the ranks behind them, the press making it impossible for the soldiers in the center to use any weapons at all, so they began arguing for including as few short weapons in the pike block as possible.

Alternatively, rather than a hollow square filled with halberds a pike block might be arranged in sort of a hamburger, with several ranks of pikemen in front, several ranks of halberders along with officers and colors in the center, and then several more ranks of pikemen behind. This allowed halberders to move out of either side of the square during a push of pike and attack the enemy flanks, but otherwise worked in a similar manner.