Back when I first started to watch college football (late 70s), I seem to remember running backs lateraling the ball to each other all the time, like three or four times in a single play. A guy would have a tackler on him, and be just about down, then he’d shovel the ball to another guy who would take off with it.
They had stopped doing this by the time I went to college (late 80s). Why? Was there a rule change? Too many fumbles?
I don’t recall a style of football with lots of laterals and I have been watching college football since the 60’s. What has changed in college football is the move to a more wide open offense with more passing and a straight ahead running game. In the 60’s and 70’s the better football teams used the wishbone or option type of offense. The power teams of the era such as Oklahoma, Nebraska, and USC relied on an offense that generally featured one very good running back and a bunch of good running backs. The first half was pound the ball at the defense and soften them up. The second half was let the star running back run over the tired defense. These teams rarely threw the ball and when they did they didn’t have much success. The real change in college football happened in the early 80’s when the NCAA limited the number of scholarship athletes that a school could have. Plus high school and college players are getting better coaching and training these days.
Defensive players are too big and too fast for option football to work at the highest levels, unless you can get offensive players who are bigger and faster. Even Nebraska has all but abandoned the option attack.
Tossing a lateral is dangerous - if it’s not caught, it’s a live ball. For that reason, it’s out of favor unless it’s done (once) behing the line of scrimmage with most defenders well blocked and the intended recipient alone and ready. It’s just easier and safer to move the ball upfield by throwing it forward or running it directly.
There is one rule at issue here, but I’m not sure when it was introduced: A runner behind the LOS who is in position to recieve a pitch cannot be “blocked” (read: tackled without the ball) below the waist. Players across the LOS can be wiped out before the ball gets to them, so if a team made a habit of running set plays with downfield laterals, defenses would likely eliminate the intended recipients of those laterals.
I’m not sure Rugby-style mutiple lateral football was very popular as late as the 70s, but, since I wasn’t born until 78, I won’t dispute the claim that that is what you saw 
Maybe the OP just saw replays after replays of The Play in the 1982 Cal-Stanford Big Game? Must’ve been something memorable to have seen on TV. I can’t seem to dig up any actual footage of it, though.
I think the OP may be talking about the option play which was used by Nebraska and Okalahoma among other teams.
Here is a site which describes it.
It isn’t as popular because defenses are much faster and stronger than they were 20-30 years ago.
Also, the influence of the pro game into college football. Plus, option quarterbacks had a rough time in the NFL. It would be hard to recruit a good quarterback if they knew they’d have to run the option all the time.
The option and the veer and the wishbone are all out of style. They are only used by teams that have serious size deficiencies. The military academy teams tend to use some version of them. They just don’t have linemen big enough to handle the pass blocking. If an undersized lineman is moving he can be put to use. But if you’ve got a 300 lb defensive lineman coming at 260 lb offensive lineman who is pretty much stationary trying to protect the QB, then more often than not the 300 lb guy is going to win that battle.
You can find what Cal fans call “The Play” on cals website, here.
I think the OP is talking about the desperation laterals far down the field and not the basic option offense. After forty yards* of a run, the player is about to get tackled and laterals to a following runner who takes it in ofr the score.
Amazing when domne right, tragic many other times, tho, when it resulted in a turnover when they could’ve settled for a forty yard gain.
The fact that it’s more a schoolground tactic than anything else causes coaches to rant against it for fear of losing the good yardage gained. Heck, even in High School, my coaches preached against it. Because it rarely seems to work out well.
*yardage for example only.
I’m afraid you’re mistaken. That style of football went out long before the 1970’s; multiple downfield laterals haven’t been popular since the 1920’s and '30’s. Coaches associated with that style were Andy Kerr of Colgate and Bernie Bierman of Minnesota; you can see some cool footage of rugby-style football in the uncut version of Knute Rockne, All American, although I don’t believe said footage actually comes from Notre Dame. The major rule change associated with the decline of the downfield lateral was the change in the shape of the ball to make it more pointy and less round; it’s easier to pass now and harder to lateral. Even wishbone and option offenses typically involve only one lateral per play; multiple laterals are seen only in dire circumstances such as when you’re behind on the last play of the game.
The relative simplicity of these offenses is also a big draw for the academies, given that the students are kinda busy preparing to serve their country and haven’t got scads of time to leaf through thick playbooks.
No, I’m sure I saw it in the 70s. Maybe I just thought it was more widespread than it really was because it makes for an exciting highlight film.
I am talking about downfield laterals, by the way, not the option or anything else that happens behind the line of scrimmage.