Is it possible to waive the debts owed by some of our Muslim brothers who are financially unable to settle them and count them as zakat?

This is permissible according to one opinion of the Shafi'is, the As-hab from the Malikis, Imam Ja'far Al-Sadiq, Al-Hassan Al-Basri and 'Ata`. The basis for this permissibility is based on the Quranic verse listing debtors among the eight recipients of zakat: “Zakat expenditures are only for the poor and for the needy and for those employed to collect [zakat] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler—an obligation [imposed] by Allah, And Allah is Knowing and Wise” [9: 60].

A charity
The fact that God calls the act of a person who absolves another of his debt a sadaqah [charity] further substantiates the opinion expressed above. God the Almighty says: “And if someone is in hardship, then [let there be] postponement until [a time of] ease. But if you give [from your right as] charity, then it is better for you, if you only knew” [2: 280].

A matter is determined according to the intention
Even though the debtor does not receive the money from this act of charity nor does he actually possess it, the elimination of the debt is tantamount to receiving it. And since it is permissible for the creditor to pay his zakat to the debtor and then take the money in fulfillment of the debt, it is likewise permissible if he absolves the debtor of his debt by deducting its amount from zakat. Thus, both cases achieve the goal which is relieving the debtor from the burden of his debt.

The ruling
There is no harm in waiving debts and counting them as zakat because this entails goodwill and facilitating matters for the debtor by relieving him of his debt. Moreover, there is no harm in not informing the debtor that his debts have been waived from the creditor's zakat as this is also an act of kindness that will lift the debtor’s spirits and spare him any embarrassment, all of which are noble meanings encouraged by Islam.
And God the Almighty knows best.