Wouldn't it have made more sense to have Jesus, when He was responding to a request from His followers to show them how to pray, not include a direct petition to God to have their trespasses forgiven?
The answer is simple, really. Because, when you go to sacramental confession, you are asking God to forgive your sins, and He is doing so through the priest. You don't need the priest's forgiveness about anything, you need God's. That's why you go. And, since you need God's forgiveness, and you seek it when confessing your sins, it is perfectly appropriate to ask for these things, both ahead of the time and after the fact, when making a sacramental confession.
Not to complicate things here, but there is another point. Strictly speaking, only "mortal sins" must be confessed sacramentally. While it is certainly a good thing to confess "venial sins" in a sacramental confession, this is not absolutely "required." Therefore, one could recite the Lord's Prayer (especially at Mass, where one's venial sins are removed by the Mass itself), combined with contrition for such sins (yes, contrition is required for all sins, even venial ones), and such sins could be forgiven at that point.
"What is the Biblical basis for the distinction in levels of sins?" you ask. The answer can be found in 1 John 5:16-17, where John makes a distinction between "mortal" sins and those which are not "mortal." Non-mortal sins are known in the Catholic Church as "venial sins." Mortal sins destroy the sanctifying grace in one's soul, while venial since merely weaken that grace. The total absence of sanctifying grace in one 's soul at death means, by definition, that the person cannot ever enter into Heaven. Thus, sin that destroys such grace is "mortal" to one's soul, hence the name.
I hope this helps answer your question! :-)
Well, it helps me to see things better from a Roman Catholic point of view.
Still, it doesn't really answer (for me, anyway) the question of why Jesus, if He intended -- or commanded -- that sins (or even a certain category of sins) be confessed through a priest to God, would respond to a request from His own disciples about the proper way to pray, and include in that prayer -- a prayer prayed directly to "Our Father" -- a request to have one's trespasses (or debts) forgiven.
Why, if Jesus commanded His followers to confess their (mortal) sins to God through someone else, would Jesus have included this specific petition -- prayed directly to "Our Father"?
Jesus could have prayed like this, when demonstrating the way to pray to His disciples: "Provide us a means for the forgiveness of our mortal sins", but that isn't what he says.
He seems to make a point, in this prayer He prays in response to His disciples' request for a demonstration of prayer, of demonstrating that the sinner may -- or should -- request his or her forgiveness directly from the Father.