You forget something.
The alternator will supply the proper voltage to a dead battery. But it will also try to recharge a dead battery like a battery charger.
This means amps. Amps create heat, Heat destroys the rectifiers and diodes in the alternator.
I get this warning with every alternator I install.
Tester
My assumption is that when people talk about a “dead” battery there are still 8,9,10 volts left, but not enough to start an engine or power accessories.
Anything below 12 VDC is considered a DEADbattery.
Look it up!
Tester
Don’t disagree at all, but only with repeated attempts, not the occasional charging of a dead battery. It probably would be worse always driving with tons of accessories over long periods of time.
My original comment was in regards to the simplified statement “A totally dead (or bad) battery simply overloads the alternator and causes premature death.”, which is not true.
Respectfully disagree. A “dead” battery is a battery that does not have sufficient power to start a car engine, regardless of how much voltage is left. (within reasons)
Then I have a story to tell you.
Came out of work. Snowing, wind, cold as hell.
Battery dead.
Get a jump, and stop at Sears for a new battery.
Install the new battery and on the way from Sears to home the battery light comes on.
Check the charging system. Alternator dead.
Tester
Happens all the time and in 99% of the time the diagnosis was faulty from the beginning and it probably was the alternator in the first place and nothing wrong with the battery.
Lots of people assume right away that it is the battery. Easier and cheaper to replace, only to find out that now they need an alternator and there was nothing wrong with the battery.
If it was me, I would go back to SEARS and ask for my old battery back. 
Yes. And voltage regulators can fail.
I have to question that running an alternator into a discharged battery will kill the alternator.
We have all, at one time or another, jump started our car (or someone else’s) and drove away with no problem. Drive a few dozen miles and the battery is charged up and OK. If the alternator could not charge a dead battery, jump starting would not work.
Tester
Yes, too high a current for too long a time will pop a rectifier. But it all depends on how the computer controls the field current, which controls the output voltage and current of the alternator.
A well designed alternator would have sufficient diode rating and sufficient heat sinking to allow it to charge a dead battery safely. And this depends on the software in the computer and on the sensors it has for data.
Thanks so much for all the great info. I unscrewed & rescrewed the side connections. He had only hand-tightened them & they had a poor connection. Then I was able to jump it off & I thought everything was okay. He drove it to work that afternoon & came home ok but by morning, dead as a door nail. It turns out that he had his headlights set to bright. When he turned the car off, the headlights went off, but the driver sideboard lights stayed on. I pulled the switch to dim, the side lights went off & smooth sailing ever since.
I’m with @Tester on this one. I tried stretching out an old battery in my 1984 Tercel. I went through three alternators before a friend told me what Tester has been saying. I swapped out the battery, put in my fourth alternator, and never had trouble again. I live where winter is cold and snowy so I have my battery fully checked each fall. If the battery is even slightly marginal I buy a new one. For me that is about every five years, on average. It’s peace of mind that I won’t get stranded and, since 1987, I have not purchased a single alternator, not even on my over 200,000 mile cars.
You should get that problem resolved, otherwise you may end up with a dead battery again. Something’s still amiss in the car’s electronics or wiring, possibly a sticking relay.
LOL!!! That is a bit of a problem, eh? 
Going through 4 alternators, I would question your ability to properly diagnose a failing alternator or battery.
Well @kurtwm2010, it was my first car, I was 21 years old, and I did NOT know anything about cars yet. That was on my 1984 Tercel and I would have to lay part of the blame on the McParts store that didn’t think to do a simple charging system check, which would have shown a bad battery. They were all too happy to keep selling me alternators (although, as I recall, some of them were warranty replacements). This is what we call “a learning experience” where I learned about diagnosing a problem and understanding how a charging system works in a car.
When my friend, a GM mechanic, enlightened me, I replaced the battery and learned that diagnostics are important. I also learned that it never pays to stretch out a battery that is at the end of its service life. Old batteries that no longer hold a full charge are a liability and cannot not only strand you inconveniently but can severely tax and damage your alternator.
So, my car redlined at 6500 RPM. According to your theory I can run it at 6500 for 12 hours without any more wear than 1400 RPM.
Go ahead and do it. Let us know what goes first, the alternator or the engine.
