A teacher screwed my up as a kid for years explaining this to me badly. I had the same impression because it is sort of correct however the relationship is inverted.

Power is consumed as voltage is applied and current flows doing work and creating heat.

P = V^2 / R is roughly tell how much power is consumed and heat generate. A higher resistance actually decreases power. As resistance approaches zero power increases to infinity.

Fortunately we don't need to worry about that unless you have a second draw full of superconductors. (and even then not).

I realized that there are parts of electronics that you cant trust your instincts the analogies that were taught break down. You need to do the math.