The volitional form is used to express a forward-looking intention made at the moment of speaking. Depending on context, it means either “let’s …” (suggestion) or “I’ll …” (personal decision).
The volitional form can be used to clearly express your will to take responsibility for an action. This use often appears when an action needs to be done and you want to indicate that you will do it.
When the goal is to clarify responsibility, the subject is often marked with が. This emphasizes that you are the one taking the action.