If you look at the technical regulations in F1, they have two main aims - ensuring driver and spectator safety, and controlling costs to maintain competitive racing.
Most of the current technical regulations are just special cases of your rule 2. Moveable aerodynamic devices are banned to prevent sudden loss of mid-corner traction (causing the car to violently roll off into the grandstands). Many of the dimensional restrictions are there to prevent the use of ground effect, for similar reasons. Wheel tethers reduce the chance of a wheel flying off and killing a spectator (something that has happened in several motorsport formulae). Restrictions on fuel composition prevent teams from using explosive fuels or oxidizers. Limits on wing sizes and aspect ratios restrict downforce, to ensure that the drivers aren't subject to intolerable g-forces.
The culture of F1 is based around a belief that there is no such thing as the spirit of the law, only the letter. Devious loopholes are applauded for their ingenuity and characterise most development in the modern sport. On the other hand, many people in the sport remember the dark days, when driver fatalities were just part of the sport. Teams and drivers understand that in the absence of regulation, the Nash equilibrium inevitably entails dead drivers and dead spectators.
The F1 rulebook isn't an external imposition on the sport, it is a document that is designed by mutual agreement between Bernie, FOTA, the FIA and the GPDA. Every word of it has been hard fought and represents the least-worst compromise between those various interests.
Unrestricted racing is a trope that is often raised by outsiders to motorsport, but the reality is that without the technical regulations, there is no racing at all, just a contest to see who can spend the most, with a mortuary full of charred and mangled drivers as collateral damage.