I teach statistical inference for honour statistics students, MSc graduate students and sometimes students from other disciplines. I choose to teach statistical principles together with technical tools. Ideally, students learn to solve real world problems by going through statistical principle first, identify a specific data analysis method second, and carry it out with appropriate technical skills with a clear understanding on what question/problem has been answered. Again ideally, students will do what should be done based on principle, not merely (randomly) pick one tool in his or her limited toolbox. One can always pick up any needed skills in the process once well trained in the first place.
My research focus on methodological developments. I strive to answer well formulated questions in applications or in statistical theory. A huge part of my effort is to identify these research problems, followed by a careful study of existing results that may have satisfactorily solved/addressed these problems. If judged based statistical principles that the existing results do not provide fully satisfactory solutions, then with some luck, I may come up with a solution together with necessary technical justifications. When the existing results are rather satisfactory, learn from them and they may provide new ideas in answer other research problems.
Overall speaking, times are never wasted as long as we leave our mind widely open.