According to Desmond Morris in Catwatching: The Essential Guide to Cat Behaviour, a cat wags its tail when...
The cat is in a state of conflict. It wants to do two things at once, but each impulse blocks the other. (emphasis mine)
Then, some pages after that, Morris talks about what he called the dilemma of the suburban cat hunting a bird on a lawn:
To start with, the open, manicured lawn robs the cat of all its natural cover, exposing its whole body to view. This is doubly damaging to its chances. It makes it almost impossible for the cat to creep near enough for its typical, close-quarters pounce without being seen. This puts it into an acute conflict between wanting to stay immobile and crouched, on the one hand, and wanting to rush forward and attack, on the other. The conflict starts its tail wagging furiously, and the same lack of cover that created the conflict then cruelly exposes the vigorous tail movements to the frightened gaze of the intended prey. (emphases mine)
That being said, your observations are probably of urban cats in this kind of conflict, in a situation where a successful attack is almost impossible. It's the conflict that makes the cat wag its tail and, as you can see, this behaviour doesn't help the cat at all.
A feral cat in the wild, in a effective attack, will not wag its tail.