An insight, some background, and a bit of supposition might bring some perspective in answer to this question.
And to simplify things, I'll focus on the Mark account.
The insight comes when we ask where prayer showed up in the expulsion of the demon. Jesus said that kind of demon can't come out but by prayer. Jesus then cast out the demon. So who prayed?
I believe the father prayed when he asked Jesus to cast out the demon (Mark 9:17-18). Jesus is God. When the man didn't find help from the disciples, he went directly to Jesus. That's the prayer.
Based on this insight, a preliminary answer to the question, why prayer and fasting are necessary, is that there are certain kinds of demons that only God/Jesus can cast out, not the disciples. So ask God to do it, don't ask men.
Now, some background. When Jesus gives the Holy Spirit, he doesn't make us as powerful as God, as if every demon including Satan must quake in our presence. Indeed, I think it all makes sense more when we look at exorcism as a matter, not of power, but of authority.
In Mark 6:7, in preparation for the Galilean ministry, Jesus gave his disciples authority over evil spirits.
He didn't give them muscles, he gave them rank. Evil spirits would still be more powerful in a tug-of-war, or in bringing sickness, or foaming at the mouth; but the disciples now were given, so to speak, Colonel rank whereas most evil spirits were Sergeants and Privates.
When considering authority, it is conceivable that the disciples might encounter an evil spirit with a higher rank, so prayer in those cases is needed to appeal to Christ, who has the highest rank/authority of all. Consider Michael in Jude 9, who was doing God's will, who was properly authorized to a task, but was either outranked, or of equal rank with Satan, so he called on God to rebuke Satan rather than using his own authority.
The supposition, then is to fit faith into this situation. I think that greater faith would not result in greater authority. No, the authority had been given by the Lord. He didn't dole out authority based on faith (or presumably, Judas would not have been given any authority to cast out demons, and doubting Thomas may have been given only meager authority). No, Jesus gave an assignment, then gave authority equal to the task.
Lack of faith could certainly keep someone from using his authority, however. Faced with an evil spirit who shrieked, convulsed the child, then made it appear that the child was dead (Mark 9:26), it would be easy to think the task was too great. (They had authority to cast out demons, not raise the dead?) Lack of faith looks at the powerful storm waters, and forgets spiritual authority, which is the command of Jesus to step out of the boat. Faith looks past the powerful flooding Jordan, and steps into the water with the full authority of God, then watches the waters part. So faith may be necessary to keep us focused to use our authority in obedience to Christ.
A second way lack of faith would matter, is the case where our authority seems to be insufficient to the task. In those cases lack of faith would lead to failure and despair, but faith would lead us to call out to God for help - in other words, prayer. In the same way that faith led the father to come to Jesus for help, even after the disciples' failure, and that was his prayer; even so the disciples, after their failure, could have called out to God in prayer, to receive God's help.