There have been many disagreements in the past about the use of stick insects and other animals as feeder food. So as a breeder of some fairly exotic animals I decided I would like to have my input in the matter, looking at this from what I like to think of as an unbiased point-of-view.
The staple diet of many animals is primarily crickets, whether the animal in question is a lizard, or an arachnid, or invertabrate. Crickets are commonly used because they are cheap to buy, common to find and can be gut loaded and ready to be eaten. This therefore gives essential nutrients to the animal eating the cricket, and so helps maintain, or improve health.
Obviously stick insects can not be gut loaded, except with the food that they like to eat and I find this is rarely of much use to the animal that will be eating it. But aslong as the vegetation the insects have been eating is non-toxic to the predator, there is no harm in the insect being eaten, it will still give some energy. As such, the safest way to use insects as feeder food is to raise them yourself from eggs, that way you know what they have been raised on and so know if they have eaten anything even mildly toxic.
So there we have a word for and against stick insects, they could be harmful, but with the right knowledge about them and what you will be feeding them to, there shouldn't be much of a problem.
Crickets can also be seen like this as they can bite and so damage the animals you are feeding them to, but generally the animals are lively enough to move before they get nipped by the crickets. But in the case of a skin shed, this is less likely. The animal will be more lethargic than normal and so more susceptible to being bitten. Obviously the simplest way to stop this is to feed the animals properly, only allowing them as much food as they can eat and removing anything that they don't. But if you fed a mantid for example, something of which a skin shed is quite stressful for, and did not realise it was mid shed, a quick nip before you can remove the cricket may be enough to result in death. If a stick insect were used to see if the mantid was shedding it is more than likely that they mantid would not be stressed to an extent that it dies.
I am not trying to say that stick insects should be used over crickets, quite the opposite. It is essential that animals that can be gut loaded are used as the staple food so that the health of the animals being fed is as expected. But to use a stick insect or 2 every so often as food for your animals could be useful, aslong as you know that it will not harm it (ie. with toxins from vegetation it has been on as mentioned).
Perhaps you could look at it as a treat, something a little different for the tastebuds!
(Similar ideas have been put forward about stick insect eggs and snail eggs, aswell as snail young as feeder food for fish. I find that generally snail young can be used as feeder food (as can the eggs) for fish, simply because anything they eat, the fish itself can normally eat! But the young should only be used while they are a few week old, as their shells can become quite hard and may damage the fish. As for the stick insect eggs, if they were laid by your own stick insects, and you have been feeding them on non-toxic vegetation then they should be fine as feeder food, other wise care should be taken when using eggs as toxins may be passed on into the eggs.)
(Care should always be taken when using anything as feeder food. If you are unsure of whether it is safe to feed an animal something, do not use it or seek professional advise on the matter. Better safe than sorry.)