My answer is, there is no good balance. You sought both, you get nothing. One has to make some way for the other.
However, if you are very highly effective, there will be rub-off engagement, vice versa is true.
In my previous school, engagement is the key to effectiveness, now, effectiveness is the key to engagement.
A fellow colleague from another workplace, told me his boss value , engagement a lot, care a lot of his staff welfare. Nope, it is not lip service, all meetings must end by 3, all official events must end by 5. While I spend 2 weeks after the school holiday starts for review and planning next year work plan, their staff are off to their holidays just 3 days in the holiday. My colleague admits her staff are spoilt now, and will suffer when their boss goes for rotation.
I ask, how is the results. She told me it is improving over the years, the staff go all out for the pupils, since they are not bothered/ burdened by admin. In fact, many managers come to their school as it is the few in Singapore where staff engagement score is an A. Those in the industry will appreciate how difficult it is to get A in they climate survey.
Didn't know there is still such wise boss around. Engagement driving effectiveness. I have seen the other too, effective robots, who are so use to process that they like what they are doing since they know what to expect.
I am gunning for effectiveness now, as my wife says, my clients have change.