Without HUP, your electrons become purely classical, "guitar" frequencies, and your theory falls apart very quickly.. I think this is rather obvious, in fact in many contexts [itex]yes it as an important thing, but people are miss using it since they don't really know where it comes from, can YOU derive it?
you do have quantization in CM, nodes in a flute, string or whatever!
you don't need and should not use HUP to derive energy levels in an atom and why it is stable! HUP is the standard deviation of measurment of momentum times the standard deviation of position is greater than hbar/2.
all we can say about the hydrogen atom is about standard deviations of it's energy levels etc, NOT absolute values!
Do you want me to call ZapperZ to step in here and judge who of you and I are correct?
\hbar \rightarrow 0[/itex] limit is invoked to re-derive classical formulas from QM. [ And that's what you are doing by completely disregarding HUP.]
"Just" stealing Schrodinger equation from QM, and doing a few calculations fails pretty quickly.. It's simply not QM anymore, without HUP..