Can politicians be influenced to back this ? Solar Roads? No more power shortages, no more roaming power outages. Idaho is trying it?

You don't seem to realize electricity most comes from CONVENTIONAL power plants, which use fossil fuels.

An "electric" vehicle is merely charged from electricity, and stores its power by using BATTERIES, which are very expensive to replace and are not "green".

Solar only works in certain areas of the country effectively. If it's overcast, it doesn't work.

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The system you are describing has a number of names. In Korea it is called an "on line electric vehicle" (OLEV.) In other places it might be described as transmitting power to electric vehicles. In California there is a test strip of roadway using overhead powerlines for the high truck traffic.

There are a number of methods that have also been tried. Wired transmission is what we have with subways and trams. Wireless transmission is possible using Induction or magnetic resonance. Additional potential benefits may also include vehicles with unlimited range, no refueling times, and over all studies have suggested it is the cheapest method to implement electric transportation. (cheaper than battery vehicles and a network of charging stations.)

But to set this up on public roadways or at rest stops would require a political consensus and a desire for public works. The US has been moving away from both of these for decades. Other than in isolated locations It is far more likely to find such cooperation and advancements outside of the US than in our national political system.

It is not so much that politicians cannot be influenced but that they have already been influenced toward supporting fossil fuels and all their uses and against alternatives. It is these sources that spread rumors that electric vehicles are costly and polluting to charge while they hide the fact that every gallon of gasoline requires 4 to 7 kWh of electricity to produce... the same energy that could power an electric vehicle further than the average petrol vehicle using the refined product.

One thing solar people forget is that it takes some kind of energy source to recharge their batteries. That electricity can come from coal fired or oil-fired plants, other solar, wind, wave, nukes, or whatever, but when you recharge a battery, that charge energy is not just coming out of the thin air.