There were probably other reasons for giving Vaggie a spear VS Lute with her sword, but it still makes me so very very very happy, from a character angle
Spears get called the king of the battlefield for pretty good reason- when you’re on a battlefield specifically, a long pointy stick is VERY good at killing people without letting them get close enough to kill YOU (extra useful if you’re not tall and don’t have much built-in reach). It’s also great for formations, a weapon that that becomes TERRIFYING when it’s a in a group. If a row of spears holds their ground, keeps their nerve, and TRUSTS each other, then they can break a cavalry charge (and WHERE did Vaggie learn to trust people...?)
Spears aren’t infallible tho, obliviously. Get past the pointy part and you’re pretty much golden… if the spear person isn’t holding a shield in their other hand
(Charlie with her shield covering for Vaggie in the finale battle my beloved…!)
Swords, they’re a more diverse group. Lute’s falls into the Versatile category- it can do many things fairly well, but not as good as something specifically dedicated to the task would be, while being easy to carry around. It’s even got a nice bit of hand protection! For dueling or personal everyday defense Lute’s sword is a great pick.
But for the battlefield? It would normally be a back-up weapon. Normally, getting that close to your opponent while carrying NOTHING ELSE would be a bad idea if, say, your opponent might be carrying a spear, or a longer sword, or any combo of side arm + shield. If on the other hand you don’t expect your target to put up much of a fight- because they’re terrified and running from you- or armed with weapons that can’t hurt you- If, in effect, you treat this like a HUNTING trip, and all you need to do is deal the killing blow… then a sword like Lute’s makes perfect sense.
What I’m trying to say is:
Vaggie uses a weapon that says she took fighting alongside her fellow exorcists SERIOUSLY, as a GROUP activity, and she was focused on being as effective as possible. (one of Adams best girls, out there in front where a spear belongs, killing thousands)
And Lute? Lute’s weapon only makes sense in a fight that’s PERSONAL- or in a battle that’s already tilted in her favor.
(bonus: in terms of metal needed and skill required, a sword of Lute’s type will generally be Much More expensive to make than a spear would be. In that sense, it’s a more ‘elite’ weapon, while a spear is more… shall we say.... Replaceable.)