Surprised no-one mentioned this. I discovered it by accident the hard way, while researching the problem that knowing about this earlier could have avoided.
Internally damaged "weak" batteries can cause observable voltage fluctuations while charging and extra current draw that can cause alternators to develop a fault and break.
Damaged batteries including formerly completely flattened batteries can to get into a state where it seems to just about work, but is actually quietly damaging the alternator. They don't necessarily appear "dead", they can be made to seemingly work, but it's a potentially damaging undead zombie-like state where treating them like the living, allowing them to shuffle around, results in problems.
The danger signs that I'd observed but hadn't known how to interpret were:
- Voltage fluctuations while charging. I mentioned in the question that I'd noticed these while connected to a battery charger. When driving, the alternator would respond to each such fluctuation by doing more work for longer, suffering excesive wear and (potentially) heat damage. Look for these while charging with a charger, not the alternator with the engine idling, since the alternator might be correcting and therefore masking fluctuations with the engine running, so no fluctuations with the alternator active might not mean no problem.
- The battery voltage never quite getting as high as might be expected. I mentioned in the question that the battery could often (but not always) just about reach 12.6V (but never higher). I took this to mean it wasn't dead, since that was easily enough to start the car, but actually, it meant the battery was always hungry for current and therefore the alternator was always doing extra work, not just increasing wear but also increasing the likelihood of system voltage fluctuation because it's never not feeding current to the battery.
- A third warning sign appears to be if the circuit voltage drops substantially while cranking the car to a start (or on other heavy load conditions). As far as I can tell from reading around (please correct me if I'm wrong), maintaining 11V or more while cranking is good, dropping below 9V while cranking is a warning sign of a weak battery.
I'd been using a relatively new (~6 months) but formerly completely flattened 'zombie' battery, that could be recharged and could start the car albeit temperamentally. My thinking at the time was, "well, it's clearly not dead like people say, since it seems to work". My alternator's voltage regulator wore out, and the alternator diodes and brushes got damaged.
The alternator eventually packed in and stopped working completely; ironically, shortly after I finally bought a new battery... Don't do what I did!
In particular, don't let all the talk of such batteries being "dead" fool you into thinking that they simply harmlessly fail. You also need to watch out for a battery harmfully appearing to work.
From the top-voted answer to the above linked question:
...when a car has a weak battery that battery will want lots of current. The current demand of the battery lowers the system voltage so the voltage regulator compensates by sending more current through the rotor. At idle, the alternator is incapable of making the needed current. Because of this the system voltage drops even more and the voltage regulator sends the maximum current through the rotor.
In this maximum load minimum speed conditions is where the wear happens. At the minimum speed the minimum amount of cooling is available from the built in fan. At the maximum load the voltage regulator will push the maximum amount of current through the rotor and through the brushes and slip rings. The brushes and slip rings get hot and with no additional cooling available from the fan they will wear faster.
