Marriage in Islam: Is it Islamically acceptable for a woman to propose to a man?

In most marriages it's the man who propose to the woman, why it's not the opposite? or on a par with each other? Is it disgraceful for a Muslim woman to propose to a Muslim man?

It's widely known that the first marriage for the Prophet Mohammad was his first and most beloved wife Khadeejah who proposed to him indirectly. Khadeejah was impressed with the personality of the Prophet and she wanted to marry him. So she sent her friend Nafeesah bint Maniyyah to probe his stance regarding marriage.

Nafeesah: Mohammad, why you are not married yet?
The Prophet: I'm not ready yet (financially)
Nafeesah: What if you don't have to worry about that and found a girl that's wealthy, beautiful, noble, and dignified?
The Prophet: Who is she?
Nafeesah: Khadeejah bint Khuwaylid
The Prophet: How is that possible? I'm an orphan and not rich while she's very noble and wealthy
Nafeesah: Yes, it's possible, I'll take care of that.

ٍSo it was, Nafeesah liaised the marriage and the Prophet happily got married to Khadeejah.

نفيسة: يا محمد ما يمنعك أن تتزوج؟

الرسول (ص): ما بيدي ما أتزوج به..

نفيسة: فإن كفيت ذلك... ودعيت إلى المال... والجمال... والشرف... والكفاية.. ألا تجيب؟

الرسول (ص): فمن هي؟

نفيسة: خديجة بنت خويلد..

الرسول (ص): وكيف لي بذلك يا نفيسة؟ وأنا يتيم قريش، وهي أيم قريش ذات الجاه العظيم والثروة الواسعة.

فقالت نفيسة: قل بلى وأنا أفعل

Also Quraan narrates the story of Prophet Moses/Mosah's marriage to Jethro/Shuaib's daughter and how she indirectly proposed to him and got married.

And when he came to the well of Madyan, he found there a crowd of people watering [their flocks], and he found aside from them two women driving back [their flocks]. He said, "What is your circumstance?" They said, "We do not water until the shepherds dispatch [their flocks]; and our father is an old man."

So he watered [their flocks] for them; then he went back to the shade and said, "My Lord, indeed I am, for whatever good You would send down to me, in need."

Then one of the two women came to him walking with shyness. She said, "Indeed, my father invites you that he may reward you for having watered for us." So when he came to him and related to him the story, he said, "Fear not. You have escaped from the wrongdoing people."

One of the women said, "O my father, hire him. Indeed, the best one you can hire is the strong and the trustworthy."

He said, "Indeed, I wish to wed you one of these, my two daughters, on [the condition] that you serve me for eight years; but if you complete ten, it will be [as a favor] from you. And I do not wish to put you in difficulty. You will find me, if Allah wills, from among the righteous."

Quraan 28:23-27

وَلَمَّا وَرَدَ مَاء مَدْيَنَ وَجَدَ عَلَيْهِ أُمَّةً مِّنَ النَّاسِ يَسْقُونَ وَوَجَدَ مِن دُونِهِمُ امْرَأتَيْنِ تَذُودَانِ قَالَ مَا خَطْبُكُمَا قَالَتَا لا نَسْقِي حَتَّى يُصْدِرَ الرِّعَاء وَأَبُونَا شَيْخٌ كَبِيرٌ

فَسَقَى لَهُمَا ثُمَّ تَوَلَّى إِلَى الظِّلِّ فَقَالَ رَبِّ إِنِّي لِمَا أَنزَلْتَ إِلَيَّ مِنْ خَيْرٍ فَقِيرٌ

فَجَاءَتْهُ إِحْدَاهُمَا تَمْشِي عَلَى اسْتِحْيَاء قَالَتْ إِنَّ أَبِي يَدْعُوكَ لِيَجْزِيَكَ أَجْرَ مَا سَقَيْتَ لَنَا فَلَمَّا جَاءَهُ وَقَصَّ عَلَيْهِ الْقَصَصَ قَالَ لا تَخَفْ نَجَوْتَ مِنَ الْقَوْمِ الظَّالِمِينَ

قَالَتْ إِحْدَاهُمَا يَا أَبَتِ اسْتَأْجِرْهُ إِنَّ خَيْرَ مَنِ اسْتَأْجَرْتَ الْقَوِيُّ الأَمِينُ

قَالَ إِنِّي أُرِيدُ أَنْ أُنكِحَكَ إِحْدَى ابْنَتَيَّ هَاتَيْنِ عَلَى أَن تَأْجُرَنِي ثَمَانِيَ حِجَجٍ فَإِنْ أَتْمَمْتَ عَشْرًا فَمِنْ عِندِكَ وَمَا أُرِيدُ أَنْ أَشُقَّ عَلَيْكَ سَتَجِدُنِي إِن شَاء اللَّهُ مِنَ الصَّالِحِينَ

القصص : ٢٣-٢٧

Obviously it's Islamically acceptable for a Muslim woman to decently (preferably indirectly) approach a Muslim man for marriage, it's rather recommended especially if the man is a decent and suitable person, more particularly if that person doesn't know much about the woman and how she feels about him, he could be interested in her as well but he may not know enough about her, that's quite common in Muslim societies especially in the non-mix ones where women have private/closed personality because of shyness and timidity while men are usually more open, it's not easy for some men to approach a woman for marriage if he doesn't know her or doesn't know enough about her, basically a person can't be loved until he/she is well-known to the other person.