Greg Schiano can’t remember the exact moment when the idea hit him. Maybe it was one night as he was sat in the hospital room with his paralyzed player, listening to the machines that helped him breathe. Or maybe it was during one of the long late-night rides back to Piscataway that followed.

“That whole time was a blur,” the Rutgers head coach said last week. “I just remember thinking, ‘Why do we have to have kickoffs? Just because we’ve always had them?’ ”

This is Schiano’s plan: Replace all kickoffs with a punting situation, including after the opening coin toss and to start the second half. So, as an example, when Team A scores a touchdown, it immediately gets the ball back on a fourth and 15 from its own 30-yard line.

It can punt it back to Team B — the most likely outcome and a safer play since the bigger collisions usually happen on kickoffs.

Or it can line up and go for the first down, essentially replacing an onside kick with an offensive play that would require more skill than luck.

Onside kicks work about a quarter of the time in the NFL, according to the website advancednflstats.com, a deceptive figure because the play is far more successful when the other team isn’t expecting it. Schiano isn’t sure if going for it on fourth and 15 is a higher percentage play — according to the same website, it’s about 18 percent or 19 percent — but success would be less dependent on a favorable bounce.

Either way, Schiano said, this is the bottom line: “It would lead to much less impact and fewer collisions, but it would still be a way to get the game started in similar field position.”

Schiano broached the idea at the recent Big East meetings, and has bounced it off coaches and officials on all levels of the sport. This is not usually in his DNA: In his 10 years at Rutgers, Schiano has spent little time getting involved in national issues, preferring to focus on his own program.

But this issue hits close to home.

“I don’t think we’d lose that much,” Schiano said, “and we’d gain a bunch for the welfare of the players.”

He knows he is battling a century of football tradition. It is amazing how much people perceive the kickoff as the most exciting play in the sport, when in reality, it’s simply not true. Most kickoffs are routine, a player running into a moving wall of flesh and helmets long before he can ignite the crowd.

Everyone, however, agrees kickoffs are the most dangerous play in the sport. The NFL recognized this with its decision to move the spot of the kick five yards back to the 35-yard line, ensuring more touchbacks and fewer injuries. Schiano is stunned that the college game hasn’t followed its lead.

“I think we’re wrong in college football,” he said. “We should at the least do what the NFL is doing — at the least. For us not to follow the league with the most research on anything? I don’t think we’re being as responsible as we should be.

“They wanted the fan excitement. But at what cost?”

Still, even with kickoffs moved to the 35, Schiano doesn’t think it’s enough to protect players. One coach calls kickoffs a “70-yard blitz,” players running at top speed inviting the kind of collision that paralyzed LeGrand from the shoulders down on Oct. 16, 2010, against Army.

The next day, on another kickoff in nearly the same spot at the New Meadowlands Stadium, Lions LB Zack Follett was carted off the field after a scary head-to-head collision against the Giants. He was released after a night in the hospital, but didn’t play again last season.

Those are far from the only injuries. A group of New Jersey doctors who study all aspects of sports safety are pushing for eliminating kickoffs in high school football, but they are meeting resistance even at that level.

This, of course, is the biggest obstacle Schiano faces: Tradition. No one likes even small changes in the game, and this is a big one. His idea requires people governing the sport to finally value player safety over fan entertainment, when nearly every decision tends to go in the other direction.

“I don’t think anybody says, ‘Yeah!’ I think a lot of people go, ‘Hmm. That’s interesting,’ ” Schiano said. “Until you go through something like we went through as a program, you’re probably not going to take the time to think about it.”

Schiano had plenty of time to think about it, in that hospital room with LeGrand and on those long drives home. He hopes other coaches will never have that time after a catastrophic injury, but has seen enough to knows if something doesn’t change in the sport, they will.

Steve Politi: spoliti@starledger.com; Twitter.com/NJ_StevePoliti