This is the opposite of the truth. The most productive people put their trust in others all of the time. We have to! Most of us have way to much going on to get it all done alone. Lean on others to help you, delegate to your subordinates and trust that they will get it done properly and on time. Sometimes letting go of control is the hardest part of developing efficient time management skills.
Imagine how much time you could free up if someone was cooking and/or cleaning for you? This is true at work too. So many managers pick through their employees' work with a fine tooth comb. Why? You hired these people, so trust them and don't micro-manage. Focus on the bigger stuff instead and watch your stress levels decrease. This will also help morale because your employees (or kids) will feel valued and trusted.