When using a SerializableInterface<> field, the object picker doesn't allow drag and dropping a game object that has a component inheriting from the target interface which makes the SerializableInterface<> a bit cumbersome to use sometimes. The current solution is to drag and drop the specific component from the game object inspector to the SerializableInterface<> in the inspector.
The same improvement could be done to the search filter of the picker which is currently unable to find components that inherit the interface (though that might be a limitation of Unity, to investigate).