It somewhat depends what you mean by "use full power".
Some airframe/engine combinations have a feature whereby the rated power following an engine failure is higher than that AEO. Following an engine failure, with the throttles in the take-off power position, then remaining engines will increase thrust to the "emergency"/OEI max thrust position.
In that case you could say that max thrust is only ever used following a failure of an engine. However, this operation is automatic and transparent to the pilot.
The only circumstances when take-off thrust should not be set with the throttles is when performance information is available for takeoffs at other than the rated takeoff thrust. If information is available then a 'flex' or reduced thrust may be used, where the thrust is reduced to conserve engine life at the expense of reduced performance. Since the reduced performance must not be allowed to infringe the certification performance minima, data is required (from OEM or other similar source) before the thrust is played with. In the absence of such information, only the rated TO thrust can be assured to give adequate performance.