Most parents love the notion of promoting self-sufficiency in their children. However, there are a number of barriers to overcome when it comes to putting the concept into practice.
Time is a common barrier. It can be simpler to make their lunch/get them out of bed/sort out their friendship problem rather than leaving these things for them to do. Somehow we need to strike a balance. Another barrier is an attitude to risk, our natural protective instinct.
We need to allow positive risks and extend horizons. If you feel decidedly nervous create a junior version for example:
Children who are anxious or fearful about approaching new social situations need to face their fears rather than avoid the situation altogether.
You can scaffold their independence by arranging various opportunities.
Parents have always found ways to make skill acquisition and self-sufficiency easy for children to master.