As far as I understand, the primary reason why an electron doesn't fall into a nucleus is that, when it gets close, it has a sufficiently high probability of having a lot of momentum to get back to its original position. This high probability, in my understanding, arises because the electron is confined to only a small amount of space around the nucleus, and hence, by Heisenberg's Uncertainty Principle,the uncertainty in its momentum is high, which in turn increases the probability of the momentum being large.
In such cases, where the electron "bounces off" or "phases through" the nucleus, the momentum would always have a non-zero magnitude, and hence the kinetic energy would always be non-zero. This way, energy would be gained with each new "bounce". Additionally, the electrons would be constantly accelerating, radiating away light of all frequencies.
Is my premise incorrect, or is it the implication? And in what way is it incorrect?