Why is only one generator stated in literature for elliptic curve group P-256?
You are correct. 
All points in a prime order curve (except $\infty$) are generators of the whole group.

But for practical applications a specific one must be chosen to make protocols work.

For example, Diffie-Hellman works only if the two public keys are computed as a random multiple of the same generator. 

So it make sense that, among the curve's parameters, there is also a chosen, fixed, base point.

You are free to design protocols with alternative generators, but, as any point (except $\infty$) is as good, it makes no sense for interoperability purposes.

For P-256 the choice of the generator, like for the curve's parameter $b$, is done using a deterministic algorithm with a (supposedly) random input seed.

Other curves might have different way of choosing it. For example curve25519 uses the point with the lowest absolute value of $x$ belonging to the large prime order subgroup.