Because Homer is only present in the town and in Miss Emily's life for a short while, it could seem that he was not a major character. That would probably have been the perspective of the townspeople. They might have thought that their disapproval had gotten through to her so she broke it off, or that he had decided to leave her.
The lapses in rational logic that seem associated with the townspeople are both necessary to the plot and to the author's overall attitude toward them. They don't investigate the odor, they don't insist she pay taxes, and they generally ignore her rather than try to help with her apparent agoraphobia. Are they polite or neglectful?
But Miss Emily was not eccentric, she was seriously ill. Homer as a real, live man would not fit into her fantasy relationship. Homer's specific attributes may not have been that important to her in that she apparently needed a symbolic husband more than a real one.