Here by coherence conditions I mean those axioms imposed on associators and unities that grant that the groupoid generated by such morphisms is a poset, i.e. any two parallels morphisms in this groupoid are equal. These condition implies that such weak structures are equivalent (in a suitable sense) to strict ones.
That said, where does these conditions come from? There are some deep reason, maybe motivated by some applications, for which these conditions are required?
One possible answer just for monoidal categories is that these conditions made the monoidal product more similar to the cartesian product (requiring that for every two $n$-products in the bi-category/monoidal category there's a unique isomorphism of the groupoid generated by the associators and unities).
There something similar that can be said about bi-categories?
Thanks in advance to anyone who will answer.
Edit: After reading the Zhen Lin's comment and Berci's answer I realized that this question need more specifications.
I'm aware of the fact that these axioms allows to prove the coherence theorem, which exactly says that the groupoids generate by associators and unities is a poset (as said above). What I'm really looking for is reason for the coherence at all. As I said I'm also aware the coherence provide equivalence of bi-categories/monoidal categories to strict ones, so I guess my question should be
Why do we really need that this structures are equivalent to strict ones?