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There should be no random inspections. There are only 20 cars on the grid, for the top form of motorsports not checking ALL cars is pathetic.
At most, only the cars likely to score points could be inspected; that the first 10. A thorough inspection takes time, and that's probably why the FIA limits it to only a few cars.
All Podium cars should be inspected after every race. No excuse for alleged 'top' form of motorsports. Heck, the Daytona 500 winning racecar is impounded for a whole YEAR and put on display (with splattered bugs and all) for fans. If that happened in the opening race of F1, Wheatley would instruct Min to brake-check anybody on the last lap to 'earn' second so that their dream machine would not be impounded.
IIRC they do ''basic'' tests on a number of cars after every race and 1 random car in the top 10 for a FULL check. Additional cars may be checked if sensors suspect something. Full checks granted take up a lot of time. But IMO at least 1 random car from every team should have a ''basic'' test and if one of them fails, other one should immediately be checked as well, of course.
It's questionable if a full check can be done at all, given a finite amount of resources. Some parts of the technical regulations are not exactly trivial to enforce.
F1 has the resources. Any racing league resources are finite - not a valid excuse for a multi-billion$ enterprise. How F1 uses these resources or not uses them is important. ALL racing teams try to cheat - that's how they get ahead of the competition. Its whether they get caught or not. Certain leading cars should be fully scrutinized: Polesitter (checked right after winning pole - there is only one car and you have a dozen F1 tech guys standing around), Podium winners (on long flights - cars can be checked in a separate cargo plane while heading back to UK - no time lost for teams - What an extra $100k in expense @ for 6-8 races for F1 admin? this is a rounding error in RB budget. yeah, that budget ), random cars as fits into the season. In a couple of the US car series and one motorcycle series, the scrutineers are in an open garage for all the see, in some cases a team rep is allowed in, in other cases can only observe. I dont access Sky, but this openness is not obvious in F1.
You are suggesting to check wether a car conforms to each and every article in the time between Q3 and R? Or in a moving airplane? I'll just assume that you have an extremely dry sense of humor...