I'm with you, James. I've just written an essay in which I quote Feynman.
He speaks directly to your point:
It is important to realize that in physics today, we have no knowledge
of what energy *is*. We do not have a picture that energy comes in
little blobs of a definite amount. It is not that way. However, there
are formulas for calculating some numerical quatity, and when we add
it all together it gives "28" - always the same number. It is an
abstract thing in that it does not tell us the mechanism or the
*reasons* for the various formulas.