Freebase Dali

Sound IS frequency. The sound you're taking out will be comprised of a range of frequencies in the audible spectrum. When you completely reduce the decible level of the frequency range a sound is made of, you're removing the sound. You can achieve this either by phase cancellation of those frequencies (which is what I suspect your 'noise floor' is doing, albeit a quicker method since it bases the freq range to remove on the actual sound's freq range without you having to do any sweeps manually), or simply by reducing the decibel level of those frequencies with an equalizer.
You just described what I already said.

The problem arises when the offending sound's frequency range is shared by intended signal in a recording. Removing the frequency range, by whatever method you wish to call it, will also remove that same frequency range from the intended signal, as it's a single recording and you can't separate each element after the fact, unless you're doing mid/side processing and the intended and offending signals occupy separate spaces in the stereo field widely enough so that one can be eliminated without affecting the other.

This is all standard stuff in the audio engineering world.
I'm just trying to let the OP know that the effect needing to be achieved can be done without need for an automated process if she doesn't have access to one.