I am not a grid engineer. However, ...
Unless you are genuinely designing for it, a 1-MW load can't easily get turned on and off instantaneously. If nothing else, the inductance of the wires will limit how quickly you can ramp the current up/down. EV charge equipment doesn't instantly start charging at its maximum rate - a modest ramp is employed. There are relatively small facilities, called "frequency stabilization services", whose job is to rapidly (almost instantly) respond to modest changes in supply and demand. They can hold the line temporarily while the rest of the grid adjusts. There has always been some "inertia" built into the grid that can absorb moment-to-moment mismatches. Some of it is the spinning inertia of all the turbines at generating stations. There is distributed inductance and capacitance in the grid itself: that giant mass of cables and connected equipment . Increasingly, it's batteries - including batteries co-located at EV charging stations to smooth out grid demand.
But in the end, even a 1-MW change in supply or demand is tiny compared to a local grid, which could be sloshing 1,000 to 50,000 MW. For context, the grid has to respond to an entire power plant, or a critical substation, going offline more-or-less instantly with no warning. That could be a change of 100 to 1,000 MW. These things happen more often than you might think - and yet you never notice.