Good article. We have two camps; 1) The World which is enmity with God. The World we can consider as Godless. 2) God-fearing people.
No amount of argument from the God-fearing camp will have much influence on God-less people.
The question of Euthanasia is of concern to God-fearing people. Old people who are in severe pain and close to death, we would like their suffering to be short. The power of prayer can be very effective when the prayer is asked aright. As it is said; (James 5:16)The effectual fervent prayer of a righteous man availeth much.
In times like these where there is severe pain and death is expected, I think praying to God has its place. The prayer should not be made requesting the person is made well, but that the person's own prayers be answered. The one who is in pain (assuming they are God-fearing) would be to ask for relief and an end to suffering. This is asking God to bring their life to a quick end to spare suffering the pain. In such a condition there is no quality of life, and where death is inevitable due to having lived to a good age beyond our three score and ten, then is seems right to ask God to make the suffering short. If a person requests God to shorten their life and not prolong the agony, I would request God to hear and answer the person's prayers.
Where there is no belief in God by the person suffering then why should God intervene with the natural process; all be it painful? God will answer the prayers of a righteous person, but the prayer must be asked in the right way and for the right reason. There are many times when God has answered prayers and replied to the person suffering or to the one appealing on their behalf.
Without God, the World will continue to argue on this matter.