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Spears let you get a 3rd rank to be in range, which you'd naturally end up being in a position to do that with a 40-man blob.

If you've got, say, a 10-man wide unit of 20 swords, they should all be able to attack if you get mugged by 3 palladors, but not against a Warboss or smaller (at least in the first round).
But if you're doing so with 40 spears, you could easily get ~32+, after piling in and all that.

20 4's & 4's would give 5 wounds to save against,
32 5's & 4's -"- 5.3

And since you've got more spears hitting, they get a greater benefit from the warlord's Gnash Gnaw ability (+1 attack).

I'm also finding it way more common to end up bunching rather than keeping neat, wide lines, but as soon as your rats start dieing, you get to the small unit sizes where swords start doing better than spears.