Of course we pray that God might elect to save all the world. It is foolish not to ask.
Now...will God choose to save those who I ask Him to save?
Only God knows. I don't presume upon God that my plans for someone's salvation are God's plan.
The prayer of a righteous man availeth much, but not necessarily for the salvation of those who are dead in their sins. Prayer changes the mindset of the prayer rather than changing the mindset of the prayee. God doesn't change. We change. We receive the mind of Christ.
I don't presume God's plans for general things are my plans either. And God will not force lost people to accept him.
But God said to pray for the lost. He said to pray expectantly. Jesus said to pray for your requests over and over - persistently and gave the parable of the persistent widow.
When I pray, I pray God's will. God said three times in Ezekiel alone that he takes no pleasure in the destruction of the wicked.
If God created billions and billions of people - hating them as he created them - creating them as reprobates never to have an opportunity to be saved - created them ONLY to burn in hell forever - then that would be his will that he watch them burn in an eternal bonfire while he smiled upon the torment.
But that's not what the Bible says. God does NOT take pleasure in the destruction of the wicked. Why? Because the Bible says it is HIS WILL that none should perish.
None means NONE. Of course, billions will perish because they reject God - like Cain, who rejected God's personal plea for him to live right and be "accepted". Like the rich young ruler rejected Christ outright.
Because God takes no pleasure in the destruction of the wicked and his desire is that none should perish - I pray for the lost with great expectation. Like Moses did when he prayed that God would spare the people of Egypt and God relented. I am NOT comparing myself to Moses - only explaining how I pray.
I believe that God WANTS my Muslim students and their families to be saved. I believe that God WANTS my gay friends to turn from their wicked ways a be saved. I pray that way.