Your right that doesn't work with physics, not even a little bit.
It's the kind of stuff a star trek engineer would be proud to spout. Still that is the advantage of writing your own stuff, you can just make things up.
Tech will change and new things will be found out, but to paraphrase Scotty 'You canna change the laws of physics!" that reasoning on why solid shot wont work is so fundamentally wrong it's painful. So the work to counter KE doesn't stress the generators, but the energy release when a beam hits does stress them. To counter the KE of the sold shot you will need
at least the same amount of energy, "Energy can neither be created or destroyed" and so on.
Take an 18" naval shell (say 1,500lb or ~700kg), accelerate to 0.1c. The shell now has a KE of 350PetaJoules. All that energy hits the shields and something has to happen to it, that is a fundamental law of the universe.
Or you just don't bother with explaining it and take the answer used about how Trek inertial dampers work, 'Perfectly well thank you.'