inorganic chemistry - Why doesn't water play a role in reactions in aqueous reactions?

$$\ce{Ba(NO3)2(aq) + Na2CO3(aq)}$$

In the above reaction both the substances are in water, however water plays no role in the reaction. Why is it that although water is present in the reaction, it does not play a reactant role? To clarify, why isn't the above written as:

$$\ce{Ba(NO3)2(aq) + Na2CO3(aq) + H2O}$$

Why does water act as a bystander and not a reactant?