I don't think Tbpiper imagines that at all! In fact, I agree with him that we have full access to the Throne of Grace through Jesus Christ, our ONE Mediator. Paul's prayers for others and his asking others to pray for him had to do with having a personal investment in the lives and ministries of other brothers and sisters in Christ. Unlike the un-Scriptural idea of praying TO the dead, imagined "saints" or not, this kind of prayer actually works to strengthen our faith and draws us closer to each other, edifying the body of Christ. Sending prayers into the mist towards those we can never know are hearing them really does nothing to encourage our faith IN Christ.
Does God know what we have need of before we even ask for it? Yes, He does. So, prayer is for OUR benefit - to strengthen our faith and trust in our gracious Heavenly Father, who loves us and delights in blessing us. We hardly need a back channel like asking Jesus' mother to nag Him for something He may hold back because He is such a meanie. That is the kind of attitude that results from praying to dead people for favors. THEY get the glory if or when something happens, instead of God, to whom belongs ALL glory, honor and praise. No human deserves what belongs to God alone!
Not only do we have full access, but we have a command to seek God's help for one another. NOWHERE are we told to pray to dead people to gain the ear of Christ, our ONLY Mediator!
James 5: 13 Is anyone among you in trouble? Let them pray. Is anyone happy? Let them sing songs of praise. 14 Is anyone among you sick? Let them call the elders of the church to pray over them and anoint them with oil in the name of the Lord. 15 And the prayer offered in faith will make the sick person well; the Lord will raise them up. If they have sinned, they will be forgiven. 16 Therefore confess your sins to each other and pray for each other so that you may be healed. The prayer of a righteous person is powerful and effective.
17 Elijah was a human being, even as we are. He prayed earnestly that it would not rain, and it did not rain on the land for three and a half years. 18 Again he prayed, and the heavens gave rain, and the earth produced its crops.
19 My brothers and sisters, if one of you should wander from the truth and someone should bring that person back, 20 remember this: Whoever turns a sinner from the error of their way will save them from death and cover over a multitude of sins.