> In my work we are constantly giving people chances to take on more responsibility,

In my experience, this means one of two things:

You're asking people who already have too much to do, to add even more to their plate.

Or

You're throwing the projects which are doomed to failure and nobody else will touch at them.

In basically every job I've ever had this has been the case. There is nothing like being given a shit sandwich and being told it's delicious ice cream.