To be fair, Nick didn't act like any potential engagements were dependent on the dads' permission. In his conversation with Raven's father, Wes, Nick asked if he'd be "comfortable" with him and Raven getting engaged, though he didn't exactly ask for a blessing. The moment was ruined, though, when Wes told the camera, "I feel like there is a good possibility it could be Nick that I hand her off to," in reference to his daughter. Fathers walking their daughters down the aisle at weddings is contentious already; the poor choice of wording emphasized the idea that women are "handed off" from one man's possession to the next. And that's the same issue with asking for "permission" in the first place.
When Nick and Raven sat down with her parents, she said that her father "taught [her] what to expect from a husband." It's sweet in terms of admiring her parents' relationship, but also creepy given the show's overarching father/daughter dynamic here.
Still, the old idea of fathers being the gatekeepers of their daughters' relationships loomed over the episode. Before Nick and Corinne sat down with her family, Corinne told the camera that her mom and sister would like Nick, but she mimicked the gestures of a stern, gruff man to symbolize her father's reaction. (Corinne's father later told the camera that "any dad would naturally have concerns" about Nick.)
In Vanessa's case, she noted to the cameras that it was "very important" to her that her father approve of her future husband. Nick actually asked Vanessa's father if he'd have his "blessing," to which he responded, "I just can't give you my blessing, just like this." Vanessa's dad then grilled Nick further, asking if he'd sought the three other fathers' blessings, too. "It was similar, yes," Nick responded. He did give Nick his blessing in the end, but not before calling into question what the idea of a father's "blessing" even meant, in Nick's case.
There's nothing wrong with involving your family in your relationship, and asking your parents for their opinion on potential partners. After all, they've known you your whole life. But in that case, why not involve both parents, instead of just bringing your father into the conversation? The tradition of asking for permission is cringe-worthy, not to mention heteronormative.
And it's clear that the Bachelor engagements would go on regardless of what the fathers told Nick. So why does it need to be such a big part of the hometown dates? The episode would have been dramatic enough with family members' concerns about people getting hurt, or not knowing Nick. Focusing on the father's blessing is outdated, and it doesn't need to be a Bachelor tradition.