You used Einstein's equation for v=0; the rest-mass/energy equivalence.
If you use Einstein's full equation, there is no "striking analogy."
Your definition of kinetic energy excludes photons, which have kinetic energy and momentum but no mass.
Yes, a photon's energy is all kinetic but so what? Newton's equation specified massive bodies.
Again, the 1/2 is BS but the winner of this debate is still to be determined.
Newton's equation specified massive bodies.
Ergo, Newton's equation does not apply to photons.
Einstein's equation does apply to photons.
Ergo, Einstein's equation is not Newton's equation.
For velocities much less than the speed of light, Einstein's equation is well approximated by Newton's equation.