Given that a properly-functioning pitot-static system is absolutely essential for flight (a plane cannot be flown without valid airspeed data, or at least not for long), are there aircraft that automatically check the functioning of the pitot-static system before liftoff? This seems like it would be quite easy to do; during takeoff, compare the airspeed measured by the pitot-static system against the groundspeed (which could be read from speed transducers mounted on the landing gear), and sound an alarm (“INVALID AIRSPEED” or something similar) if the rates of change of the two fail to match within a certain tolerance (indicating either a failure of the pitot-static system or severe windshear along the length of the runway, both of which necessitate rejecting the takeoff).
First of all, ground speed is already determined by the IRU’s. No need for landing gear sensors although most airplanes do have WHEEL SPEED transducers for anti-skid currently installed. Wheel speed is not always equal to groundspeed but can be at times. For example, wheel speed right after takeoff is different than ground speed because the wheel begins slowing the second it leaves the ground.
Second, airspeed changes with altitude. So, the higher you are the faster your airspeed. This means that taking off in Death Valley might show a different airspeed RELATIVE to groundspeed than in La Paz El Alto.
Third, most of the time, airspeed doesn’t register correctly until about 60 knots. You’ll see that most airspeed indicators have 60 knots as the lowest indication mark. This is because if the airplane is pointed into the wind, it could register spurious readings. So, before any checking gets done, the plane needs to be moving above 60 knots.... Like during takeoff.
Fourth, airspeeds are cross checked during takeoff roll. The vast majority of airspeed splits on a new flight leg occur on takeoff roll and result in a rejected takeoff - your premise anyway. Occasionally it’s not noticed until takeoff. This is rare. The other instances (which I work on more frequently) are in flight malfunctions usually related to inadequate pitot heating.
Fifth, the current system works very well. No need to reinvent the wheel.
Comparing it to ground speed won’t work. If there’s any wind the two won’t match.
On airliners there are multiple pitot systems. Usually one displayed to the captain and one to the first officer and often a backup. Failures are detected either by the aircraft systems or the pilots themselves cross checking their readings for a mismatch.