Is it a good idea to do without the last output capacitor before transforming?Of course, there is nothing in the academic definition of an opamp that prevents it, or make it particularly suitable to a specific task.
Driving a xfmr implies a few constraints, such as current capability commensurate with the xfmr characteristics and output expectations. Low offset is to be considered, since it can result in doing without teh dreaded output capacitor.
Couldn't even the slightest current in the transformer generate noise?