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Once you adopt the work-in-the-past idea, can't you drop the restriction
about "conservative" forces?
There's lots of non-conservative force fields in the world. Don't they
do work, too?
In particular, the "electric power" sold by the electric company is
almost always traceable to non-conservative fields in a dynamo
somewhere.
It seems to depend on how you define "system." If a "non-conservative"
force does work on a system then the sum of KE and PE of the system will
change. Isn't that why we call a force "non-conservative" in the first
place, though we don't define "non-conservative" this way?