I haven't got any objections to feeding live fish to my charges. I do have a problem when people feed fish feeders that are too large subsequently causing the feeder to suffer unduly. However, that's besides the point.
Most fish that are predatory have some capacity to crush with their throats, their gill rakers have rough or toothed pads on top, and you'll often see them moving their throats in and out rapidly to scale and crush their prey. Granted, it's still far from an instant death, but far better than repeated dismemberment and panic.
Remember too, that fish don't really want their prey to be chewing on their insides once they get there either, so they do their best to disable the prey beyond that capacity.
Large, predatory fish eat other fish in the wild, and at times, their instincts are too difficult to over-ride. If they can be weaned onto artificial foods, great, but if not, feeders it is.
One point that another poster on here mentioned was that eating a whole fish would be unpleasant for the pets. I don't think that's necessarily true, in fact, that whole fish (if in good health), would provide all the right nutrients required for the pet to grow, heal etc. moreso in fact than a lot of the cheaper lines of pellets etc., or even the cocktails of frozen food some feed to their pets.
Frozen and dry foods are certainly more convenient for the owners, but caution must be exercised to provide all the essential nutrients to the pets. I don't believe a fish's enthusiasm for a certain food type indicates the fact that it's absolutely better for the fish e.g. Discus getting constipated on a diet too heavy in bloodworms. It's quite easy for larger animals to die of malnutrition without ever starving.
So, in summary, feed feeders of a suitable size to your pets if need be, and do not labour under the mis-guided view that pellets/dead food are the only way to go about giving your pets what they need. Above all else, it is our pets we're looking after, not just our own comfort.