I would never think or expect an electronic (non mechanical switch) throttle lock to remain locked after the radio has been turned off and power cycled. This isn't logical in my opinion. On the other hand, a trim setting I would expect to hold in memory after a power cycle.
What isn't logical about that? What limitation would that pose to anyone using it? How does it become illogical if it remains locked until unlocked. Many things in life are like that.