When ourselves or someone else is in a difficult situation, we just pray and think that God will do the thing for us and we just have to sit back and relax. But I think that's not the philosophy Jesus taught us.
Think about it. If Jesus had just prayed for the salvation of the mankind, wouldn't had they been saved. Why he chose to go through an actual sacrifice?
well, I don't think that and I am sure many many other believers do not think we just pray and think it's a done deal
on the more serious side of things though, you state Jesus CHOSE to go through an actual sacrifice
two things regarding that
1. it was God's plan to redeem mankind and Jesus obeyed God...it was not something He chose to do..what He chose to do, was to obey God...if you read of Jesus prayer in Gethsemane, you will find that Jesus actually said that if possible, He preferred not to be the sacrifice...and then He went on to say, but God's will be done and not His
I hope you see the difference there because basically, God asks the same of us...He asks we do His will and not ours
2. it is God's will that everyone be saved, but not everyone will be saved
we are told to 'continue' in prayer...that is until we receive an answer...there are different kinds of prayer
it's all in the Bible