It is generally understood that seeking the permission of a father to wed a daughter, in most cases in our current culture, including in our churches, is absurd. But this is not because in-and-of-itself it is contrary to biblical precepts. It is absurd because, in MOST cases the potential bride (and prospective groom) have had little, if any, interest in the views of the father up until that point. Most times, the bridal prospect has been considered "too old" to give considerable credence to parental influences for years prior to "seeking permission." The prospective couple is generally seeking blanket agreement with their autonomously-arrived-upon intent.
This is NOT how those honestly trying to apply biblical precepts would approach the matter. I was involved with one pair of families who agreed upon the importance of parental involvement (in general), and paternal authority/responsibility (in particular). They saw each as indispensable in the marriage decision-making process. The following marriage "ceremony" model was intended to properly reflect the responsibility and authority of the parents involve.
After prayer, the minister/pastor shall say, "Who giveth this woman to be married (to this man)?
Bride’s Father: I do.
Groom’s Father - to the father of the Bride: As [Bride’s Name]’s father, having raised her, watched over her, guarded her, and loved her - and having opportunity to diligently assess the merits and weaknesses of [Grooms Name]’s character and means - have you determined it to be God’s will that you release your daughter from your direct headship, and the watchcare of your home, for the purpose of [Bride’s Name] joining with [Groom’s Name] in the covenant of marriage - [Groom’s Name] then being [Bride’s Name]‘s head, under Christ?
[Bride’s Father’s Name]: Yes, I have.
[Bride’s Father’s Name]: [Groom’s Father’s Name], as [Groom’s Name]’s father, having raised him, watched over him, counseled him, and loved him - and having opportunity to diligently assess the merits and weaknesses of [Bride’s Name]’s character and abilities - have you found her to be a godly young woman and determined it to be God’s will that you counsel your son to pursue [Bride’s Name]’s hand in marriage?
[Groom’s Father’s Name]: Yes, I have.
[Bride’s Father’s Name] shall place [Bride’s Name]'s right hand into [Groom’s Name]'s right hand.
[Groom’s Father’s Name]: [Groom’s Name], Will you take [Bride’s Name] to be your wedded wife, to live life with her after God's commandments in the holy estate of marriage? And will you love her, honor and cherish her, so long as you both shall live?
[Groom’s Name]: I will.
[Bride’s Father’s Name]: [Bride’s Name], Will you take [Groom’s Name] to be your wedded husband, to live life with him after God's commandments in the holy estate of marriage? And will you love him, cherish and obey him, so long as you both shall live?
[Bride’s Name]: I will.
Fathers step aside.
Pastor continues in the service by administering the vows, and ultimately declaring the marriage covenant entered.