The extra electricity needed for EVs is zero or maybe even negative

That's unlikely to be the case, the US already does use batteries in power production and the amount more we would need to switch all US power to solar would be astonishingly high.

Power plants can’t react to the amount of power needed at any time and they get inefficient trying

They can't react in the minute by minute basis, but they do react to usage. Most coal fired plants only operate at about 50% capacity most of the time and bring on reactors to match the predicted power usage curve. When building a power curve profile the power company typically takes into account constant power as a baseline (solar and hydro being always on during the hours it is active and the power output of a given number of reactors is relatively set). Power is then supplemented with smaller generation sites which might use natural gas or even petroleum products. The smaller sites are far less efficient and make less power, but the name of the game when making power is making sure you always have enough for demand.

Let's say it's peak day, 25 solar farms are making 675 MW right now, each coal plant reactor can make 500 MW and the demand right now is 1250 MW. You start up your natural gas turbine plant to make up the difference during peak day, but as the sun goes down you start up reactor 2 and 3. As reactor 2 and 3 get going the power usage goes up to 1600 as people come home and the solar farms stop generating power so you continue using your turbine plant but also start drawing from your batteries. Once reactor 2 and 3 are up and running you might stop using your turbine and keep drawing from your batteries, but when people go to sleep the power usage drops to 700 MW. Now power usage has dropped but you keep the reactors going for a while or begin to shut them down (they will still make some power as they shutdown) to recharge the batteries.

All these numbers are hypothetical, but it's a description of how the process works.