Of course it's possible. Most processed fish foods, even the low quality ones, have a much higher percentage of protein as live foods for example. But that is not the same as necessary, or better. It's basically a fish farming argument. Produce the biggest yield with the smallest or cheapest amount of food.I am no expert on this, but I'm sure a quality pellet or flake food can have better nutritional content in it than live foods for your fish. Less chance of dragging parasites and disease into your sealed box of a tank as well.
We're talking about pets here. If you want the best for your fish (again talking about general small community fish here) the order is this:
1 live foods
2 frozen live foods
3 processed foods
Incidentally, that is identical to the fishes preference (see Althena as example in this thread ..)
There is no danger of bringing in diseases with live foods as long as they are not collected from bodies of water with fish in it.
Having said that, you can safely feed your fish just Tetra foods, just realize it is a convenience, not better or tastier for the fish.