Usually if someone thinks a character is useless in any way, you can try to think about them not being there, and seeing how quickly the narrative will fall apart or have to completely change its scope in that character's absence.
Without Kat, Dante would have still been asleep when the Hunter demon attacked. If he managed to live through the initial attack, he'd beat the Hunter Demon, get out of Limbo, and then have no place to live, and Dante's life would pretty much continue as a slightly obscure and hedonistic fashion.
Vergil still could have gotten Dante to join up somehow, and I imagine Vergil would have to be the one making portals for Dante to travel through. Things would change pretty drastically without Kat's involvement.
Beyond that, Vergil would have had no way of knowing how to get to Poison in the Virility factory (Kat was the one who found it, remember), so an attack on the factory would have been different. When the Order got raided, Vergil would have been stuck in Limbo, and no one would have been able to copy files and set up the self-destruct sequence, so Vergil could have been killed there (possibly). Dante would probably end up being much more ruthless and without Kat to act as a moral compass, could have killed Lilith and the spawn outright, left Vergil to die at some point. Plus, without Kat, they would have had no way of knowing how to go through Silver Sacks towers, meaning the Nephilim could die on their way up, or never even attempt to storm the place.
Ultimately Dante could have killed Vergil in their final battle, or joined him in ruling over humanity. Or...he could have just never given a sh!t whatsoever, and never joined up with Vergil at all >.<
I don't think Kat is particularly useless in any way, other than fighting. However, there are plenty of different ways one can be useful in a battle, and it's not always about brute force or being on the front lines. Kat plays a pretty heavy role in the Order's war on the demons, but also as Dante's moral compass. Sure she's on the sidelines, but much of where Dante has gotten would never have been if not for Kat.
Kat's more akin to someone like Mei Ling is to Snake, rather than being the femme fatale. She's a support character, but she's given a lot of importance.
And remember, Kat was never written nor intended to be a romantic interest for Dante.
Oh, and it's desiccated
squirrel semen, not bats
