You're taking it way too literal. Some women think it's romantic when you ask their father for permission to marry them. If she wants you to do this, she'll likely tell you. The same way you'd discuss whether she wants her father to walk her down the aisle. These practices aren't necessarily bad or toxic.

If you are in a healthy committed relationship you talk about these sorts of things, there's no right or wrong. On the other hand, I do agree with you that it would be really weird and creepy to ask a father permission to marry his daughter behind her back.