Still incentive the energy savers to make investment to save more, so they can sell more rights, and incentive the biggest energy consumer to consume a bit less so they pay less.
Part of the emission trading concept is to reduce the number of certificates in circulation overtime to increase the energy saving incentive („cap and trade“). The government can do this by buying certificates or reducing the amount free certificates assigned every year. The details are a bit more complicated but were implemented already over ten years ago in the European Union. There is simply no need for an additional carbon tax if this scheme is maintained well.