I am unclear what the benefit of forcing the number of slots to be a prime number.
As you say, the distribution may not be evenly distributed, that is why.
True, but will modulus prime be better than any other modulus at distributing the items amongst slots.
I can see why an even modulus might give a bigger bias than an odd modulus e.g. if the least significant bit of the hash was always 0, but I cannot see why a prime modulus >2 would give any better distribution than any odd modulus >2.