In my experience, at some point or other, a Christian dating couple usually gets the parents involved somehow, whether it's by asking permission, having a meeting, discussing their plans, etc., etc.
I'm not saying every Christian couple does it, but it's a good idea. In my experience, yeah, a guy will express his feelings for a girl, she'll reciprocate, and then the guy asks the Dad first if he's OK with it.
I mean, one of the most basic biblical commands is “Honor your father and mother” (Eph. 6:2) That's a broader command than the command to "obey" them we see in verse 1. It's be good to wait for their parents’ blessing. I think it's worth waiting for even if you end up waiting a long time. But probably not forever. And we should communicate to our parents that we desire their blessing.
I get that this tradition is "cultural," but that doesn't mean it's old-fashioned or foolish. Why would it be foolish? In
1 Corinthians 13:5 Paul says that love
"does not behave rudely, does not seek its own, is not provoked, thinks no evil" Now, that word "rudely" here (or "unseemly") means that love doesn’t "blow off traditions," if you will. Or unnecessarily despise cultural mores and customs.
Yeah, a lot of Western marriage traditions are only traditions. Kinda like wedding traditions, like the white dress, the church ceremony, walking down the aisle, etc., etc. Do you
need to follow all these traditions? No. But I think that if you live in a culture where these traditions are valued or expected, the you need to have good biblical reasons for doing things a different way.