Is it permissible for a wife to travel alone by plane from her home country to America to join her husband residing there, given that it is impossible for a mahram to accompany her, and is this considered a necessity that permits a woman to travel without a mahram?

If you are unable to go to your wife or find a mahram for her, and you are in need of her to protect yourself [from sin] and care for your children, then there is no blame in permitting her to travel to you without a mahram. She must take precautions by traveling with a trustworthy group, and you must know the day of her departure and her time of arrival.