As others have somewhat noted, the problem with passing in F1 is not really the turbulence produced by the leading car. It's the effect that the turbulence has on the aero-balance of the trailing car.
An F1 car's handling is very sensitive to shifts in the aero C of P, which can occur when the front wing or underbody momentarily produces less downforce due to turbulent airflow. The instantaneous rearward shift of the aero balance produces loss of grip at the front and severe understeer. The driver of the trailing car cannot see the turbulence so he can't react to it.
Maybe the FIA should develop some sort of synthetic vision aid for the driver's visors that give them a real-time, visual display of wake turbulence flow. At least that way they might be able to avoid it. It might sound far fetched, but modern aircraft have warning systems that are somewhat similar.
MotoGP bikes aren't impacted by wake turbulence from a lead vehicle because they are designed strictly for low drag. Their handling is all coming from mechanical grip (plus how big the rider's cajones are
F1 cars will always have front and rear wings with huge, flat end plates. Those wing end plates are the most valuable part of the car, since that is the best place to put sponsor decals. The teams would never agree to get rid of a piece of composite that likely generates over $1000 per square inch in sponsor cash.