Prime order elliptic curve groups: Generators and the reason choice
Yes, by Lagrange's Theorem in the group theory, the order of any element must divide the order of the group. Therefore, except for the identity element, which has order 1, all other points can be a generator.
If you define a protocol, you need a common agreement and the generator is a part of this. If you don't include it in the specifications you need to agree for every user. Instead of this, one point is assigned as the basepoint.
Normally the base points are selected in the manner of nothing-up-my-sleeve-numbers to show that there are no backdoors designed. The choice reason is given as

The generators of G1 and G2 are computed by finding the lexicographically smallest valid x-coordinate, and its lexicographically smallest y-coordinate and scaling it by the cofactor such that the result is not the point at infinity.

BLS12-381 is used for digital signatures and zero-knowledge proofs in Zcash, Ethereum 2.0, Skale, Algorand, Dfinity, Chia, and more.