I'm not entirely sure if I agree with this. It is understandable what you are saying; but when speaking, to my knowledge vowel reduction is huge. And it can make or break your conversation. You say that it is more important to pronounce the consonant correctly.

What about the verbs:

бить

быть

Both of the vowels are following a hard consonant. And if they mean entirely different things, so it seems like vowel reduction would be very important.