The days of the supercars in NASCAR were dying by then - they were far too fast for the safety measures of the time, and NASCAR limited the winged cars to 305 cubic inch engines after 1971.
I think the best place to would have been Trans-Am. The series hit its peak in 1969 and 1970, with Camaro vs. Mustang vs. Challenger vs. Javelin being played out all across America on road courses, and had the energy crisis not set in, we may have had a few more years of the original musclecars before the Mustang II, the ugly-nose Camaro and the ends of the Javelin and Challenger.
What might be a result is that street stock racing with musclecars catches on as a result of Trans-Am, thus focusing American road racing around tin-top style cars. Hence, Mustang, Camaro and Firebird on the track during the Group A era of the 1980s, creating yet more awesome Group A racing of the time.
Imagine it - the late 1980s could have seen all of these in one touring car field:
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Chevrolet Camaro IROC-Z (5.7-liter V8)
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Pontiac Firebird Formula (5.7-liter V8)
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Ford Mustang GT (5.0-liter V8) or
Ford Mustang SHO (2.3-liter turbocharged inline-4)
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Ford Sierra RS500 (2.0-liter turbocharged inline-4)
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Toyota Supra Turbo (3.0-liter turbocharged inline-6)
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Nissan Skyline GT-R (2.6-liter turbocharged inline-6)
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Mitsubishi Starion ESI-R (2.6-liter turbocharged inline-4)
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BMW M3 (2.0-liter inline-4)
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BMW M635CSi (3.5-liter inline-6)
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Audi Quattro (2.2-liter turbocharged inline-5)
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Mercedes-Benz 190E 2.5-16V Cosworth (2.5-liter inline-4)
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Holden Commodore VN Group A SS (5.0-liter V8)
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Lancia Delta Integrale (2.0-liter turbocharged inline-4)
Can on imagine?

With a field with this much diversity, how much would one bet that Group A touring car racing would still exist?
The musclecars as a breed were losing a purpose by 1971-72. But should they change form, into straight-line demons which would also haul arse on any corner they find, they'd have more a future.
If this seems like a thread hijack, my apologies.