Why do people commonly ask other people to pray for them?

When someone pray and the other said "amen" and then the praying is as if the two or more person do pray.

If someone considered to be holier or righteous than us, then the more chance our hope more acceptable by God.

Look how the leper asked Jesus to pray to God for his health. Since Jesus was a holy prophet then the more likely the pray is more acceptable by God.

.....The leper answered: 'I know that thou, Lord, art a man, but an holy one of the Lord. Wherefore pray thou to God, and he will give me health.'

Then Jesus, sighing, said: 'Lord God Almighty, for the love of thy holy prophets give health to this sick man.' Then, having said this, he said, touching the sick man with his hands in the name of God: 'O brother, receive thy health!'.....

'For with the heart believes unto righteousness and with the tongue confession is made unto salvation'.

Romans 10:10

I believe this applies to prayer. God knows in your heart what your every need is but we need to speak it.

If you pray about other person's concerns, you show that you care about her.

Jesus asked His disciples to pray for Him at the hour of His greatest need - in the garden of Gethsemane. They failed to do so, but God the Father sent an angel to minister to Jesus instead. This proved that the Father had heard the Son's anguished prayer and so responded where human support failed.

Jesus needed courage to face His time of suffering, in order to complete the will of the Father. He faced an ordeal not just of physical pain, but of knowing He would become sin and so the Father would have to forsake Him for a time. He prayed earnestly but although His disciples let Him down on that score, the Father heard and answered.

Jesus also told us to keep on seeking, knocking and asking, and it would be given. We dare not presume on God's mercies! We ask, we knock, we seek - in faith - and when we feel weak or disheartened, the supporting prayers of others can help us persevere. Have a read of Matthew 7:7-12.

And prayer is primarily our worship of God, communicating in faith with our Heavenly Father - we do not always ask Him for things. We just adore Him out of a heart overflowing with love for Him. Prayer is for our benefit, to help us grow in faith and to draw closer to God. However, there are times when prayer support of others is needed. In James chapter 5 a sick person can call on the elders to pray over him, to anoint him with oil in Jesus' name "And the prayer offered in faith will make the sick person well; the Lord will raise him up. If he has sinned, he will be forgiven. Therefore confess your faults to each other and pray for each other so that you may be healed. The prayer of a righteous man is powerful and effective." AiH

We pray because it works Yes, God may know what we want or need, but it helps to ask.

Perhaps, it is because they have forgotten to pray.

Probably cause it requires no work. But, people have died while letting other people pray for them rather then seek medical help.