It is permissible to demand an exorbitantly high amount of mahr.
The evidence is the verse of the Quran which mentions a husband having given excessive dower to his wife:
وآتيتم إحداهن قنطارا فلا تأخذوا منه شيئا
And you have given one of them a great amount [in gifts], do not take [back] from it anything.
— Quran 4:20
There is a tradition that Umar ibn al-Khatab once gave a sermon in which he imposed a limit on Mahr, but then he changed his opinion when a woman disputed with him and presented this verse as proof.
Following are some extracts from the exegesis of the verse:
قوله تعالى : وآتيتم إحداهن قنطارا الآية فيها دليل على جواز المغالاة في المهور ؛ لأن الله تعالى لا يمثل إلا بمباح
The saying of Allah: "And you have given one of them a great amount" is evidence for the validity of excess in Mahr, for Allah does not give a (positive) example except of a permitted act
— Tafsir al-Qurtubi
وفي هذه الآية دلالة على جواز الإصداق بالمال الجزيل
This verse is evidence that is permitted to give excessive wealth as mahr
— Tafsir Ibn Kathir
It has been mentioned that there is no disagreement on it being permissible:
وقد أجمع العلماء على ألا تحديد في أكثر الصداق ؛ لقوله تعالى : وآتيتم إحداهن قنطارا
There is consensus of the Ulema that there is no upper limit on Mahr, because of the saying of Allah: "And you have given one of them a great amount"
— Tafsir al-Qurtubi
ليس للمهر حد أقصى بالاتفاق
It is agreed upon that there is no upper limit on mahr
— الفقه الإسلامي وأدلته