Friction (grip) is directly related to pressure between two surfaces so one can argue that narrow tires have more grip because more pressure is put on the ground through the smaller contact area. If a narrow tire has a contact patch of 1 square inch, a 200 lb rider will exert 100 psi to the road. With a wider tire, perhaps only half or a third of that will be exerted. In real life, though, irregularities in road surface will have a significant effect on how well a tire grips. The bigger factor is the compliance of the tire with the road, and on most surfaces the higher pressure narrow tire will "bounce" more losing contact as it does. Lower pressure wide tires have a shock absorber effect that better modulates contact with rough road surfaces.
Also, wider tires may not use more electricity. They may have a bit more rolling resistance, but again that depends on road surface, but rotational mass may be the bigger issue. Heavier wheels will certainly take more energy to accelerate; however once up to speed, they have more rotational momentum that "stores" more energy than a light wheel. Think flywheel here.
This sort of hypothetical musing is fun, but I think tire width choice should be a compromise seeking the best combination of comfort and rolling resistance. There are some very nice supple wide tires available.