@brabdulmuhaimin In these situations it's important not to rush to a conclusion based on a handful of Hadith based on limited exposure because there may be others, and the understanding of them may not be in line with your own opinion. So you've done the right thing to ask.

@brabdulmuhaimin The Hadith you mentioned about the ring was in the case of a man who had nearly nothing to be able to get married with and therefore the prophet asked him if he at least had a ring. This was not the man offering just that but the prophet looking for a solution for him.

@brabdulmuhaimin When you look to the majority of the narrations on this topic you will find that the mahr is almost always attributed to being hers or the like of the women in her family or women like her, it is not attributed to the decision of the man.

@brabdulmuhaimin This is then reflected in almost all books of fiqh after this. So women have the freedom to ask whatever they want and men have the freedom to offer whatever they want and people who are sincere about marriage will meet somewhere in the middle that is easy for both parties.