How do you think the context demands your view rather than what "debt" actually means? I don't see how you justify ignoring the legal understanding of debt.
For several reasons.
First, Scripture repeatedly tells us to forgive one another as a condition that God will forgive us (Ephesians 4:32, Matthew 6:15, James 2:13, etc.). If the "model prayer" is speaking of debts in a financial-legal sence then this is the first occurrence.
Second, it is contrary to other passages dealing with repaying financial-legal debts. We are not to charge interest, however we are to give to those whom legal payment is due.
Third, forgiveness is essential in the spiritual aspect (forgiving trespasses). Jesus tells us, as stated above, that God's forgiveness is conditioned on us forgiving others. That the "model prayer" would deal with forgiveness in an entirely different manner and ignore so much of Scrioture is possible, but odd.
Fourth, considering this a debt in a financial-legal context rather than a transgression against God places God as vulnerable to man. I believe God is immutable and complete (granted, my own presupposition,, but it prevents me from entertaining your view).
Fifth, this debt is used in two situations - asking God to forgive our debts as we forgive the debts of others. This would have a very narrow application of only in a financial-legal sence. In a broader context, the one I believe, we are all to forgive those who wrong us as God forgives us for doing wrong.