Actually, in this era of digital voltage meters, I measure Vth, not Rth.
Vth drops from well over 9.0 V for a new battery to 8.8 V for one that is
showing its age.

I was under the impression that the open-circuit voltage wasn't a
reliable measure of how much "juice" is left in a battery.

It wasn't back in the days of analog meters with 10% accuracy. It is now
that we have digital voltmeters with very high input impedance and 1%
accuracy.