As I understand it, work is not done by the kinetic energy. Rather the
force of friction, acting in the block, does work, the effect of which is
to reduce the kinetic energy of the block - essentially to 0, if the
plate is massive enough. The work done by the reaction force, acting on
the plate, has the effect of increasing the internal energy of the system,
to the extent that the kinetic energy imparted to the (very massive)
block is negligible. Under those circumstances, dU = K (almost).
Al Clark
PS. I believe the "internal energy" is normally used to refer only to the
energy of atomic motion with a material, not to the macroscopically
measurable energies. One could use it to refer to the total energy of a
system, if you wished, in which case the discussion would be different.