They didn't ban the body, they changed the engine specs. They would have to have banned the Superbirds and Daytona Chargers, too. They were even more aerodynamic.
Back when they could run 426 Hemis and Boss 429s, they were breaking 200 mph on the straights. That's with late 60's early 70's technology. Scary!
Cale Yarborough drove a Cyclone in 1970 and qualified at 194+ mph at Daytona.
Also in 1970 Buddy Baker broke 200 mph average speed for qualifying at Talladega in a Daytona Charger.
In 1971 they limited the "special cars" to 305 in^3 (Superbirds, Daytona Chargers, Mercury Cyclone, and Ford Talladega) and their speeds fell 12 mph or so.
I believe in 1974 they limited all engines to 358 in^3 ending the era of the "big block" and restrictor plates were in common use by 1988 at the superspeedways.
Some of the details may be off a year or two but you get the gist.