Why do we use [H⁺] and [OH⁻] in balancing redox reactions instead of using [H₃O⁺] and [OH⁻]?
It is by far not universally agreed upon. My year 10 chemistry teacher taught me to use $\ce{H3O+}$ in balancing. The result is a larger number of water molecules on the other side of the equation but everything else is the same.

Many chemists will prefer $\ce{H+}$ because it is shorter and simpler, that’s all.