Why Mahr is given by the husband?

Mr Ghamidi writes in his tafsir under 4:24
یہ مہر کیا ہے؟ مردوعورت نکاح کے ذریعے سے مستقل رفاقت کا جو عہد باندھتے ہیں، اُس میں نان و نفقہ کی ذمہ داریاں ہمیشہ سے مرد اٹھاتا رہا ہے، یہ اُس کی علامت (token) ہے۔

But the classical Islamic literature has a very strange concept of Mehr, giving an impression that it is given for fulfilling one's sexual desires (like in prostitution)
For example,
قَالَ يَا رَسُولَ اللَّهِ مَالِي‏.‏ قَالَ ‏"‏ لاَ مَالَ لَكَ، إِنْ كُنْتَ صَدَقْتَ عَلَيْهَا، فَهْوَ بِمَا اسْتَحْلَلْتَ مِنْ فَرْجِهَا
You are not entitled to take back any money. If you have told the truth, the Mahr that you paid, was for having sexual relations with her lawfully
(Sahih Bukhari)

أَيُّمَا امْرَأَةٍ نُكِحَتْ بِغَيْرِ إِذْنِ وَلِيِّهَا فَنِكَاحُهَا بَاطِلٌ فَنِكَاحُهَا بَاطِلٌ فَنِكَاحُهَا بَاطِلٌ فَإِنْ دَخَلَ بِهَا فَلَهَا الْمَهْرُ بِمَا اسْتَحَلَّ مِنْ فَرْجِهَا
Whichever woman married without the permission of her Wali her marriage is invalid, her marriage is invalid, her marriage is invalid. If he entered into her, then the Mahr is for her in lieu of what he enjoyed from her private part.
(Tirmidhi, hasan)

Also the name Mehr itself is disgusting because the same word Mehr is used for the money given to a prostitute woman.
نَهَى عَنْ ثَمَنِ الْكَلْبِ وَمَهْرِ الْبَغِيِّ وَحُلْوَانِ الْكَاهِنِ ‏.‏ يَعْنِي بِمَهْرِ الْبَغِيِّ مَا تُعْطَاهُ الْمَرْأَةُ عَلَى الزِّنَا
forbade the sale price of a dog, the earnings of a prostitute and the earnings of a fortune teller.

By the earnings of a prostitute he meant what a woman was given for fornication. (Muwatta)

Also the verse 4:24

فَمَا ٱسْتَمْتَعْتُم بِهِۦ مِنْهُنَّ فَـَٔاتُوهُنَّ أُجُورَهُنَّ فَرِيضَةًۭ

Here again the Mehr is linked with fulfilling one's sexual desires, that when you have fulfilled your desire then pay money!

Verse 2:237 also makes Mehr half when no desire is fulfilled.

This concept of Mehr in my view is so impure and so similar to prostitution that it destroys the sacredness of Nikah itself.

As far as I have studied, Islamic literature has no mention of Mehr defined as "a token of bearing responsibility". Please share if there's any. It is only defined as اجر الاستمتاع . Giving money for fulfilling one's desires, ( like in prostitution).

I would be really grateful if Mr Ghamidi responds to this criticism, especially how he sees and interprets the quotations above...

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