We set the crossover to 80hz in AVR. Why should we bother what low frequency the speakers can produce ??

We set the crossover as 80hz in AVR. That means, it is not sending any frequencies below 80hz to speakers.
A crossover isn't a brick wall; that's just the frequency at which the response starts rolling off. So even if you set the crossover to 80Hz, sounds below that frequency are still being reproduced by your speaker (albeit more quietly). So the speaker should be able to produce clean/undistorted sound below the commonly used 80Hz crossover point.
 
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