Here's the issue: the engine manufacturers are also one of the most important financial sponsors of the sport. You'd need to convince Mercedes, Ferrari and Renault to build obsolete engines and put down a big bag of money.
And besides, you won't be able to fit a big V8 engine under the bodywork of a current-gen F1 car with the narrow coke bottle shape at the rear.
The engines are also pretty damn impressive, running at 50%+ thermal efficiency. Ye olde pushrod V8 would run out of fuel at half race distance with current fuel regulations.
70 years of iteration on a basic design goes a long way.
The engine would have to put out about 7 mpg at 110 mph average speed, with lots of braking and acceleration and top speeds north of 200 mph.
It would need a turbo and significant amount of boost to put out a comparable 850 hp. And not exceed 100kg/hour fuel flow rate.
And it's still about 60kg heavier at about 150kg vs. 210kg.
All of this is kinda a silly comparison, because an LS engine won't fit in an F1 car and afaik can't be used as a stressed structural member.
But in all honesty, you have to hand it to the old American V8, it is at a hell of a local maxima.
You could stick a commodity pushrod V8 in there and make 1000hp easy with a bolt on turbo and run the same laptimes.
Nothing else on earth is close to the aero.