If DNA were that much of a factor, Joe Montana’s sons Nate and Nick, at least one of them would have made it in the NFL. Both did play football in college, Nate at a few different schools, and Nick played fairly well in two seasons at Tulane. Neither were drafted or played a down in the NFL. I can't find a link but I seem to recall hearing Nate made no attempt to get into the NFL, and after getting into trouble as a teenager, basically focused on completing college and moved on with his life. Not sure if Nick even attempted to walk on to an NFL team.
Some people may recall Jack Elway playing college at ASU, following in the footsteps of his father, and grandfather. He did okay, but he too had some issues in his young adulthood getting arrested once, didn't have what it took, or that much interest, and left football. He has completely moved on now, running a high end hat making company and not having much of anything to do with football.
I recall hearing something once about baseball pitchers. A manager or scout of an MLB franchise once said that who you were, who you were related to, who you knew, even who coached you growing up, all didn't make a lick of difference. If you were a young player in even an obscure college, even a tiny independent minor league, and you could throw a 90mph fastball with any accuracy at all, they'd find you. And it wouldn't take years to do so. I imagine the same applies to football. If you are a QB in high school and have a strong arm that's fairly accurate, and show a real interest in learning and growing, you've got a chance, regardless of who your parents were.
Final story. When I went to high school there was a super athlete named Derrick Glenn (I may have gotten his name wrong). He ran track, and played football, mostly as a wide receiver or tight end. But he was big, and fast with great hands. A men among boys. We thought he was the next Jerry Rice (showing my age here!). Well, he got out of school and went to the University of Nevada, mostly because of their coach, Chris Ault a hall of famer who developed the pistol, and he knew he'd get a real chance there. Well, he got to Nevada, and joined the squad with all the other "next Jerry Rices". He played some, did okay, never bad, never great. Didn't get drafted. Tried to walk on with I think the 49ers, didn't get anywhere, and that was it.
As Stan Brock told me, the difference between the best and worst players in the NFL is "this much" holding up a tiny gap between his massive thumb and forefinger.