Acts 6 shows us the legitimacy of delegation, even in the context of the church. Pastors can’t do everything, for example, and it is right to have a team of people that you delegate areas of responsibility to.
But Acts 6 also teaches us that mere delegation is not enough. You have to delegate to competent people that are actually capable of doing good. Note, for example, how the apostles were not careless in who they delegated the food distribution to. They delegated it to capable men, individuals of “good repute and full of the Holy Spirit.”
Now, listen. It’s easy to go wrong here and think that good character is enough. It’s not. The people you delegate to must have character and competence. To delegate to someone who has two hour devotions every day (which is not even, by itself, a mark of true Christian character) but doesn’t know how to serve well (or have the willingness to learn) is not right. It is, in fact, irresponsible.
I would in fact argue that true Christian character actually manifests itself in the desire and quest to become competent. Not everyone is a star right out of the gate, and we need to give people opportunities to learn and grow. But if someone has demonstrated incompetence over a sustained period of time along with the lack of desire, or inability, to learn how to carry out their function well (to those working under them just as much as those who work above them), continuing to delegate to them is irresponsible. It is not the model of Acts 6.
As Christians who care about loving and serving others, we care about truly helping people, and not merely making noble attempts. That means that it’s not enough to delegate to “someone.” We must delegate to able, competent, faithful individuals.