The role of the guardian in the marriage of a woman predates the current Shariah. From the Quran we have evidence regarding its existence in the time of Lut عليه السلام and Moses عليه السلام:
قال هؤلاء بناتي إن كنتم فاعلين
[Lot] said, "These are my daughters - if you would be doers [of lawful marriage]."
— Quran 15:71
قال إني أريد أن أنكحك إحدى ابنتي هاتين
He said, "Indeed, I wish to wed you one of these, my two daughters..."
— Quran 28:27
Similarly from ahadith we have evidence of its existence among the Arabs during Jahiliyyah:
أن النكاح في الجاهلية كان على أربعة أنحاء فنكاح منها نكاح الناس اليوم، يخطب الرجل إلى الرجل وليته أو ابنته، فيصدقها ثم ينكحها
There were four types of marriage during Pre-Islamic period of Ignorance. One type was similar to that of the present day i.e. a man used to ask somebody else for the hand of a girl under his guardianship or for his daughter's hand, and give her Mahr and then marry her.
As for the marriage of Khadijah to the Prophet ﷺ, note that Khadijah could be the one who wanted and suggested marriage however the actual contract was done on her behalf by her guardian, i.e. either by her father Khuwalid ibn Asad, or by her uncle 'Amr ibn Asad - the opinion preferred by some scholars is that it was the uncle and the father had died beforehand.
أن عمها عمرو بن اسد زوجها رسول الله
Khadijah's paternal uncle 'Amr bin Asad married her to the Messenger of Allah
— Tarikh al-Tabari
As for expressing the wish for marriage to a person by a woman then that is also permissible in our Shariah (see islamqa), however that does not exclude the role of the guardian. Hence the marriage of Khadijah was in compliance with the Islamic tradition.