My husband had a chat with my dad, which I knew about in advance and was fine with. Iirc it was just a quick thing while doing other stuff, not a formal lunch. If Dad had some sort of bizarre tantrum and said no, it's not like we would have called it off lol.

I never saw my dad as a "gatekeeper" and I'd been living on my own for about 15 years by that point.

It was just a nice gesture from my husband to my elderly dad. Less, "do I have your permission" (ick) and more, "I'd like your support in this marriage and to be welcomed into the family."

OP probably knows their girlfriend and this dad the best, and in this relationship and family it's considered a nice gesture.

If/when your daughters are ready for marriage I imagine they and their partners will talk about what traditions to keep and what to discard.