The particular work-energy theorem that you are using in the first part of
your instructive analysis is the one that is often called the
"pseudowork-energy theorem." It equates the change in bulk translational
kinetic energy of a system to the integral of the net external force
acting on the system over the parallel component of the motion of the
system CM. As Bob has noted, since MA < MB and you are explcitly
performing your analysis in the system CM frame, the CM of MA moves
farther than that of MB by a factor MB/MA during the time that the force f
acts. Thus, we find that your |WA| = (MB/MA)*|WB|. Indeed, this agrees
as it must with what you find independently from analysis of the kinetic
energy changes with the help of conservation of momentum. So there really
is no problem with these works. They are well defined and calculable
without further information.
As you note, however, the *thermodynamic* work (what Harvey Leff and I
call the "system specific external work" and which is equal to the sum of
the integrals of each individual external force over the parallel
component of the motion with respect to the system CM of its point of
application. Hard to say carefully enough in words! See the paper) on
each block cannot be calculated for such frictional interactions without
impossibly detailed information about the interaction.
I don't really want to dispute your contention that the word "work"
(especially as it is commonly and sloppily used in conjunction with
frictional forces) is generally ill-defined, needlessly confusing, and
often useless. But I would like it better understood that it is
*possible* to be precise about which definition of work we are using in
any specific application and which system energy change it is connected
with.