Correct, hydrogen and electric are merely media to transfer power from the reactor to your vehicles or other remote consumption devices.
Thing is, hydrogen can be made almost for “free” as you cannot throttle a nuclear reactor and the reaction continues to “burn” at a constant rate (more or less) at night when demand is minimal. Right now, all that power is going to waste, but if you could set up a hydrocracking plant next door to make hydrogen, you’d get hydrogen for cars at no significant additional energy expense.
And the only byproduct of hydrogen combustion or use in a fuel cell is water.
You are incorrect in how a nuclear power plant is operated. It can be throttled back, just not quickly without problems. Also electric utilities tend to keep the nuclear plants fully loaded and shut down and/or lower other plants during lower demand times.