How to reduce car traffic- Short Trip Congestion Charge

Consider these three things:

• There has been some plans to base insurance fees or taxes on vehicle miles travelled. The less you drive, the lower your fees or taxes.
• Bikeshares usually give you the first 30 minutes for free. After that, you'll have to pay.
• A lot of trips made by car are short. So short that a bike could be used instead.

Combined, they become the Short Trip Congestion Charge:

• A gadget in the car measures the trip
• Unlike the bike share, the first two miles cost you extra. The first mile will count as 5 miles for counting the insurance fees / taxes. The second mile will count as 3 miles.
• after that, 1 mile = 1 mile

Short trips by car would cost more, making people want to walk and bike more. Of course, there's a big downside to this: there's no gadget to do this at the moment, and people would have to pay for it. But I think it could be an useful tool to stop people making ridiculously short trips by car.

Does the idea have any obvious faults that I haven't thought about?