The soul is like the CPU. The brain is like the motherboard. The eyes/ears/etc. are like peripherals.
The soul may be the seat of consciousness, but a CPU will not function well if the RAM is not working properly, or if the signals it's getting from the webcam are scrambled.
It's true we observe personality changes if the brain is damaged, but it's harder to say if this is because the soul is somehow also damaged, or if what we see is fallout from the damage to the interface between the soul and the physical world. Personality is shaped by experience, and what a soul experiences is shaped by any number of environmental factors, including hormones, drugs, and physical injury.
I decided that in my fictional world, disembodied minds cannot think.
I think this is fine if that's the way you want to go. An alternative take would be that disembodied souls either don't interact with the physical world at all (Christian perspective), or interact in some totally alternate way that doesn't need a brain.
It could also be that a soul is normally capable of thinking by itself, but trying to think with a damaged brain is like trying to think in a room with loud noises and obnoxiously flashing lights; too many distractions. Alternatively, maybe they experience time in a totally different manner, such that from its perspective, a disembodied soul can think just fine, but trying to "map" that into our physical reality falls apart somehow without the help of a brain to "mediate".
The soul does have senses beyond those of the body and can form vague, hazy memories of its experiences in this "afterlife" state, but it needs to be bound to a new body with a brain or the equivalent before it can think again and reflect on its memories (and the "incarnation" process may destroy some of the memories).
Again, I could see going whatever direction you want. Maybe a disembodied soul experiences time differently, and so doesn't need "memories" pe se (like in this question). Once tied to a body, however, it relies on the brain for memory storage and retrieval, and so has no knowledge of extra-corporeal existence or (if reincarnation is a thing in your setting) past lives.
It's worth noting I've seen a number of settings where humans have this limitation but some other species does not, and members of that species do retain memories from past lives.
What about your fantasy world?
Fantasy world? This question applies equally to the real world. We still don't understand how consciousness works. Who's to say that you or I don't have souls? Plenty of people still believe that we do.
Does brain damage also damage the soul, or does the soul regain full functionality when freed of its fleshly prison?
Who can say? For your fictional world, I think you could take whichever answer you prefer and run with it.
why have brains?
Why have a motherboard in a computer? The brain is the interface between the body and the soul. Without the brain, the soul would have no senses, no way to control the body. We see this clearly in the case of brain damage, or even just age.
p.s. I cannot recommend strongly enough reading HPatMoR, not just because it's an excellent fanfic, but because it asks exactly this question and comes to the opposite conclusion. (As it happens, I disagree with its conclusion.) For an alternate take, I recommend the Ender's Game series, especially the later books. (I'd read Ender's Game, Speaker for the Dead, Xenocide... and I don't recall if the Card's revealed the juicy bits by then or if you have to read Children of the Mind also. Although Ender in Exile technically happens in between those, it was published later, so in theory won't mess with the arc too much if you skip it.)
p.p.s. You might want to also ask this on Philosophy.SE.