I submit that the problem with the halberd is not the weapon but the unit. Swordsmen are better, as they survive longer, and are thus more likely to win the combat through combat resolution. Being only marginally more expensive means that they are a much better option.
I therefore propose to cut the points cost of Halberdiers to 4/model. This is the sort of drastic cutting seen with the new Dark Elf book; it certainly worked there, making generic Warriors a much better choice.
For those hunting combat resolution, we make Halberdier Full Commands free. This represents the more common nature of Halberd regiments; other formations are more likely to be detachments, whilst Halberds tend (fluff-wise) to serve as proper regiments, and are thus more likely to have a complete command deck.
Halberdiers thus become a cheap unit with good combat resolution. Swordsmen aren't disadvantaged, and no fundamental rule change regarding state troops is carried out. No new special rules are introduced; rather than removing the weakness, we offset it.
What do you think?