Can the court reduce lawyer's fees on its own initiative?

I carefully read a Supreme Court decision regarding the recovery of legal aid costs, and it stated that the court did not reduce these costs because the party did not file a corresponding motion. But if I believe that the lawyer's fees are too high, yet I haven't filed an application for their reduction, can the court still reduce this amount on its own initiative? Is it always necessary to independently file a motion if I disagree with the amount of the other party's costs?