Is it permissible to discharge the debt of an insolvent debtor and consider it as part of the Zakat funds?

It is not permissible to fulfill the zakat obligation by waiving a debt, because zakat requires the intention to pay at the time of payment, and the loan was given with the intention of lending, not of zakat. Furthermore, zakat involves giving and receiving, whereas waiving a debt is merely a waiver, which is a protection of money. If you waive the debt with the intention of alleviation, it is commendable. However, waiving it as zakat does not absolve the responsibility, and the zakat becomes due again.