Mini races for qualifying are used in DTM and it is a crash festival. Imagine with the F1 jewels...
To make F1 cheaper, raise the minimum weight (a lot) and prohibit refueling. Cars could use less expensive materials, be tougher to resist to small accidents (like Indy), they can keep engines' development (more weight to move would accept more power, probably in a broader rpm range than today). I am not sure about tires and aero restrictions, but some modifications here and there to make overtaking easier would help.
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caugb
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