Parrots in the wild do eat insects, but they do not make up a large part of their diet. They are more likely to eat them while raise young, because insects are high in fat and protein. Nestlings require a lot of energy and protein to grow quickly. In captivity, we need to be careful about offering too much fat and protein to our companions, as it can cause weight gain and trigger hormonal behavior. Pet birds tend to be a lot less active than their wild counterparts, so rich foods need to be limited for health reasons. And many of them will show little or no interest in dead bugs.
It is also important to realize that the quality of feeder insects varies quite a bit. I have kept lizards in the past and the nutritional benefit received from the insects they consume will vary quite a bit depending on how the feeders are raised and the diet that they are fed prior to being eaten. Drying the insect also changes the profile a bit, because they are harder to eat and lack body moisture.
Ideally, offering insects that you have raised, fed, and killed yourself would be best, because that allows you to control their diet and offer them to the bird as "fresh" as possible. With dried product, you are just hoping they were fed properly and raised under clean conditions. And the dried insects are harder to eat, with a harder and sharper carapace (outer shell).
However, unless you have an insectivourous softbill species (or a pet lizard, sugar glider, hedgehog, etc), it is almost certainly not worth the trouble to raise feeder insects for your bird. The average pet parrot just doesn't need a lot of insects in their diet. As an occasional treat it is not bad, but any more than that is likely to be too much, unless the bird is molting or breeding.
So I would say "safe in moderation", but limit them as much or more than fatty nuts/seeds.