All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
First of all, we first we would like to thank your wife for adhering to your request not to treat non-Mahram men; may Allah reward her.
The matter is as you mentioned, that we have several Fataawa stating that it is impermissible for a male doctor to treat a female or a female doctor to treat a male except for a necessity or a need, and we mentioned therein the statements of the scholars.
If there is no necessary or need, then neither of the two is entitled to treat the opposite gender.
It is not correct to say that there is no difference between a man and a woman in this context because the objective is to relieve the pain from the patient and improve his health, as the Sharee’ah differentiated between them in this regard. As long as this objective can be achieved by a man treating a man, then why should we violate the Sharee’ah and let the woman do it?
Just dealing with a man and mixing with him can be a reason for temptation, even if she does not touch any part of his body or look at it, and so on. The believer, male or female, is required to seek what guarantees the safety and well-being of their religion.
Ibn 'Umar said, “The Prophet never abandoned reciting the following words in the morning and the evening: “O Allah, I ask You for well-being in this world and the Next. O Allah, I ask You for forgiveness and for well-being in my religion and in this world, and in my family and my property….” [Ahmad]
There is no doubt that the wise Sharee’ah has noble objectives by setting a solid fence in regard to women dealing with non-Mahram men. This religion stems from (dealing with matters according to) reality and not from a hypothetical idealism. The Lord of Majesty Who has created man is most aware of him, so He is aware of the instinctive inclination of men towards women and vice-versa. Therefore, Allah set Islamic conditions pertaining to the dealings between men and women, so He forbade seclusion (between a man and a non-Mahram woman), touching (a man touching a non-Mahram woman or vice-versa), looking at a woman who is forbidden to look at (or a woman looking at a man), and so on, so that virtue would prevail and vice would be avoided.
Allah Says (what means):
• {Tell the believing men to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts). That is purer for them. Verily, Allah is All-Aware of what they do.} [Quran 24:30]
• {And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts) and not to show off their adornment except only that which is apparent….} [Quran 24:31]
Usaamah ibn Zayd, narrated that the Prophet said: “I am not leaving behind me a more harmful trial (temptation) for men than women.” [Al-Bukhari and Muslim]
Also, Abu Sa’eed Al-Khudri, narrated that the Prophet said: “This worldly life is sweet and green (alluring) and verily Allah is going to make you generations succeeding one another so that He may try you in respect of your actions. So beware of the beguilements of the world and those of women, as the first temptation for the children of Israel was through women.” [Muslim]
For more benefit, please refer to Fataawa 357841, 317464, 88843, 123505, and 142487.
Allah knows best.