My initial thought is that insect wings don't rotate, and so can't destroy themselves so easily. Cheap, powerful rotational motors comes with the risk of potential for self destruction.

Flapping at that scale is a very hard problem. Apart from the microscopic flagellum, evolution never managed to produce a rotational motor since it's super hard to build decoupled components with biological hardware (you need two stomachs, hearts, etc to keep decoupled parts alive). Emulating a fly's actual method may be interesting research, but motors are probably better in the long run than flapping, a complex and difficult hack to the problem of flight.

Flies have an exoskeleton which, unlike the quadcopters of our engineers, have many flexible parts. This is much like the cage only in a very different configuration. I don't know about the wings in particular, but I can imagine they are more flexible than brittle and may even be capable of growing scar tissue.