Electrons don't "water hammer", at least not in the nonlinear way that fluids can. Aside from contrived systems, current flow is entirely described by linear wave equations (and electron flow, by thermal drift; but actual electron flow in conductors is highly irrelevant for the most part).
Water hammer is most directly analogous to flyback from switching a coil. There is some current flow, then it stops abruptly; the pressure shoots up in response. The peak depends on a number of factors (rate of change, capacitance and resistance), and the flux (pressure * time) depends on the length of the pipe (effectively, the inductance, as a pipe is more of a lossy transmission line than a general wire).
Which no one's accused of damaging a battery.
The idea about mechanical stress... is right, to a certain degree, but
so far off as to be considered
fringe.
In short, I think you will find the coupling factors are around, I don't know, something like 10^8 too small.
When we reason about multiple effects, we must consider the significance of each, rank them, and progressively sum up the result. When we reach an adequate explanation, we have no need to consider further effects. Especially when the magnitude of those effects is expected to be far smaller than our remaining error so could never possibly account for the difference. We can still find it useful to contemplate those low-order effects, in order to bring attention to them in the rare cases where they are significant, but they can otherwise be ignored, and should be.
Say we're thinking about the impedance of the battery. What contributes? Well, we might have wires, contacts, their resistance and inductance, capacitance of the battery plates over the electrolyte, conductivity of the electrolyte, ionic diffusion in the electrolyte and electrodes, etc. We can come up with a magnitude estimate for each, sum them up, compare to our measurement, and figure whether we've got a good match or not.
It might plausibly be a part of this same figure, to consider the electrostriction, magnetostriction, piezoelectricity or other electromechanical effects. (We might measure in terms of the electrical --> mechanical effect, but there will necessarily be a reciprocal effect, so this isn't a poorly motivated example.) In general, a substance will expand, contract or shear in some way when exposed to fields.
Most substances, the magnitude is so close to zero as to be ignored.
I think you will find this is the case with batteries.
Further couplings are the mechanical nature of the battery itself (if some part of the construction expands or contracts, what effect does that have on the seal?), and external influences (the cover?).
Or put another way: take a wire and a fully charged cell. Briefly short the cell. How much sound does the cell make?
Can you even tell it's making any sound at all, besides the wire sparking? (Slightly more subtle experiment, use a MOSFET and resistor so the current is more repeatable and the switch is silent without sparking.) Can you measure (say with a microphone, micrometer, interferometer, etc.) if it's moving at any magnitude or rate, that isn't consistent with, say, thermal expansion?
So, you're not wrong, but I think it's more interesting to discuss how you're not wrong, than to just dismiss your points outright.
I will however note this,
Plastic is made up of carbon, which is conductive under the 'right' circumstances.
is just out and out wrong.
Tim