The reason it does not work that way is because of how phonetics work.If I'm understanding the synopsis of the theory that others are posting, it seems like poorer acoustics should enhance the effect, since they would cause us to shift priority to our eyes to interpret.
Underlyingly, a vowel is simply a chord. There is a base tone (produced by your vocal folds), with several harmonics (called formants) above it, caused by resonance with the current organization of your vocal tract. Changing the shape of your mouth and tongue changes the formants, and so we distinguish vowels. In general, vowels are difficult to mistake.
Consonants don't generally make (much) sound in their own right. Instead, they change the formant structure. So you identify a /g/, for example, by a lowering of the second and third formants relative to the base vowel, whereas /d/ causes lowering only in the second formant.
In many cases, consonants differ in miniscule ways, so any data loss destroys reliable perception of the vowel in the first place, which in turn which breaks the McGurk effect. The effect is caused by a disconnect between what we see /ga/ and what we hear /ba/, and perceiving a consonant articulation that sits between the two both acoustically AND mechanically /da/. It only works if the sound structure is clear, otherwise you just get a huge mess with an unidentifiable consonant. The mechanical component of the illusion is there, but not the auditory one, and you need both.
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