What did Paul say? What did he say to "all the churches"?
You must follow the plain truth of Scripture. You can't rationalize it away. The issue was not cultural. The issue stemmed from Eve being deceived. Read the text. It is both a consequence of the first sin and a consequence of leading Adam to sin. The practical aspect is women, due to emotions and being created to be in subjection to men, are more likely to be led astray.
No, the roles for men and women do not stem from Eve being deceived.
God established a leadership role in Adam because he is the firstborn of men. Eve comes from Adam and has a role of service under Adam as lead curator of the Garden. Neither person is diminished. Both are image bearers of God. God simply established the lead to be Adam.
Your comment about emotions is just your own cultural hogwash and it has no biblical support. The great women of the Bible would laugh at your silly comment.
When we look at Deborah we see a shining example of a woman of God who rightly sees the leadership role to be that of a man, but she takes on the role when the man is spineless. This is hardly some emotionally dysfunctional person.
Second, men are equally led astray. In fact, the church has always had more women in the fellowship than men, purely because men are often failing to follow God as they desperately try to steer their own ship.
Frankly, your last paragraph is just silly talk from the ignorance of your faith tradition.