Tracking threads are very useful and @RyMan was very kind to come and help with your journey to IFATC. However, they are no replacement for training by a member of the IFATC team: sometimes feedback is wrong, such as here.
Moving an aircraft away from the Tower frequency is not to do with time. If there are no Radar services available, keep the aircraft on your frequency until they are clear of conflict or are departing your airspace (the first ring around the airport fix). If Departure or Centre services are available, send aircraft to that frequency as soon as is safe and proper. If Approach services are available, send aircraft to that frequency if the controller has communicated they are okay with this as soon as is safe and proper—if they are not, send them a ‘frequency change approved, good day!’
Straight out departures are not always dependent on traffic load. You may have only one aircraft on frequency but use these to not interfere with the flow of another airport (eg. the New York area). Another situation they may be pertinent despite low traffic load is with parallel runways: the only two aircraft on your frequency departing on parallel runways at the same time can cause issues with separation, for example.
Good luck with your IFATC application.