You only care about those that come at a specific angle and are reflected to an observer. For most angles it doesn't matter, remember that lakes polarize their reflection (as seen by an observer).
You could do a 5mm(+/-10nm) glass pane for it to reflect/absorb a specific wavelength but it would be hard.
It's the same effect mineralogists use with polarizing microscopes.
In a more abstract way, you're right that we are reaching for a metaphor here: if a frequency distribution is sharply peaked around one frequency then we can roughly say that the light "is that frequency" but then modify this by saying that the bits that are off-frequency, while they are "also that frequency," become "phase-incoherent" after a characteristic time or distance. That is not actually correct; they are simply different frequencies -- but it makes the interpretation easier. That metaphor begins to break down when you've got such a wide spread of frequencies: red light can only "pretend to be" blue light for a vanishing period of time.
To put it more plainly, the phase-coherence time is the inverse of the spectral width in frequency-space; multiply it by $c$ to get a phase-coherence length. If you applied it to a truly monochromatic ideal source, you would find that the time and length are infinite -- it only makes sense for real distributions with normal spread. But that's all distributions, including blackbody distributions like sunlight -- it's just that those distributions have very large spread and therefore very low coherence lengths: but it's the same definition either way.
However, if you look at sunlight at a certain time and then look at it one femtosecond later, the second look will still be similar to the first look to some extent, therefore you would have to say that the light is somewhat coherent.
This is why sunlight is definitely NOT "completely incoherent".
That leads to an equation of L= c*h / 4kT where the Sun can be treated roughly as 6000K. This gives a coherence length measured in microns, which is conveniently several times the half wave is necessary for interference for visible light (0.4-0.7um full wave). It's pretty cool, because I think it means that if you evolved eyes to see light near the peak of your black body radiator then you will be able to see Newton Rings for internally reflective thin membranes sized close to that peak due to the coherence length (due to Wien's law).
A nice review paper: http://hank.uoregon.edu/teaching-modules/Broadband-Interfero...
Therefore the "coherence answer" is exactly and precisely the correct one. What you are doing is simply explaining it with different words. "The lack of coherence" of the wave as a whole is THE argument.
What your explanation is doing is applying a narrow wavelength filter and evaluating the conditions for each \Delta\lambda, which is absolutely a valid approach, but it is the same thing. Overall I like your explanation very much, but please be careful about statements like "not really the answer, at least not directly" as they only point at a misunderstanding of the coherence explanation.
The correct answer to what question?
If the question is why we don't see iridiscence when "white" light (wavelength 380-740nm) is reflected on a "wide" film (several orders of magnitude larger than the wavelength), do you really need to talk about lack of coherence? The fact that for a particular width the film will supress/enhance thousands or millions of colors across the visible spectrum should be enough to make the resulting light white as far as human perception is concerned, I think.