I don't know of ANY Christians who do not believe in intercessory prayer.
We are commanded to pray for one another and there's always the need to pray for souls to be reached for Christ.
The expiatory suffering is another matter. But Jesus promises that when we pray the Father hears and answers and that is enough for us to come boldly to the throne of grace. I don't see that anything is needed nor is there anything that we can do to move our Father's heart more than just asking.
We can maybe feel like suffering shows Him the sincerity of our desire for the request, but all He asks of us is to come to Him with our requests. That simple.
Instead of attempting to refute me, why not visit the links with your ping list, and do as you do here, all together?