It comes down to this:
-- Some people advocate talking about energy flow.
-- Some people advocate talking about energy change, and criticize
the notion of flow.
There are many cases where it is fine to talk about energy change. Indeed
I can define flow in terms of change, plus some additional concepts:
Flow means that any positive change in a given region is
balanced by a simultaneous negative change in an adjacent region.
In more detail:
Flow of quantity X means that any increase in quantity X
in a given region is balanced by a simultaneous decrease
in quantity X in an adjacent region.
That's what flow means. That all it means. That is what it has always meant.
The laws of physics state that every energy change is in fact balanced by a
simultaneous adjacent change. That is, every energy change is part of a
flow. That's what the laws say. Period.
Now, when *you* are writing about the energy change in region A, you may
decide that you are not interested in what's going on in the adjacent
region B. That's fine. You are free to say nothing about region B, so
long as you don't say wrong things about it. Your description of the
universe may be incomplete, but it is not wrong.
However, suppose *I* am doing the writing. Suppose I choose to give a
more-complete description, mentioning the whole flow, not just one end of
the flow. The description in terms of flows is always *more* precise.
In particular, in my discussion of the emergency egress slide, the notions
of balance and simultaneity and adjacency were important. I described them
in flow-like terms. This was the right thing to do. Quite a few people
understood my description without difficulty.
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To reiterate: Some people claim that the notion of energy flow is a sloppy
shorthand for the more-precise notion of energy change. This claim is
worse than 100% wrong. It is diametrically backwards.
Energy flow does a good job of capturing the meaning of the physical
laws. Talking just about energy change is not _ipso facto_ wrong, just
incomplete. It ignores important physical facts.