Car/Monorail hybrid

Take a basic car design (4 wheels, engine, etc.) and now add an interface to the top of the car that would allow it to dynamically hook onto and ride a monorail system.

When the car is not hooked to the monorail, it functions just like a normal car. When the driver pulls under a monorail, the vehicle hooks itself onto the rail, the car's engine turns off, and the monorail computer takes control of the car. When the driver wants to get off the monorail, he/she uses the car's brakes & steering wheel, which sends a signal to the monorail computer to disconnect the car from the rail, restarts the car and returns control to the driver.

The reason I came up with this idea is that I wanted something that provides some of the advantages of a monorail--energy efficiency, increased safety, faster transit time--without losing the individuality of cars, namely the ability to buy whatever car you want and then drive it where you want, when you want.

Why would having your car on a monorail be more energy efficient? Well, first because a centralized computer is controlling the vehicles on the rail, they can be queued up close together for maximum aerodynamic efficiency. Plus, the cars would be lifted off the ground (albeit only by an inch or two) so there's less rolling resistance. Finally, the energy would be supplied from a central location, which means that the generator could be kept running at a higher efficiency than a typically maintained car engine.

As for faster transit time, on a monorail, I would expect it would be less cost-prohibitive to build "flying interchanges" in place of traffic lights.

Also, there could eventually be designated "limited access" monorail lanes on major roads. These lanes could run above existing shoulders, with occasional opportunities to enter & exit.

I could go on forever about why I think this is a great idea but I'm getting tired of trying to be coherent so I'll stop now and see what you guys think of my idea. Thanks for reading!