I don't believe that weak batteries kill alternators, unless your battery continually pulls more amperage than your alternator is rated for. I think more likely the current crop of alternators is filled with over-rated parts.
Of course a weak battery can kill an alternator. That's not the ONLY thing that kills them, and it depends on how the battery is "weak".
A battery that won't hold a charge, constantly demands heavy alternator charging current. Heavy charging current puts a greater load on--everything--in the alternator--diodes, wiring, brushes, heat sinks, etc. It also tends to boil the water out of the battery, and folks were never good about refilling batteries with water, even in the days before "sealed" and "Low maintenance" batteries became a selling point. Similarly, a battery with a parasitic drain needs the same heavy charging current, with the same results.
Point being, a stupid little parasitic drain can kill both battery AND alternator, and it's hard on the starter, and the ignition too. So, yeah, older cars with electro-mechanical clocks can have the dashboard clock kill the entire starting/charging electrical system. Thousands of years ago, that was common. Working properly, the clock would draw pulses of power from the battery--not enough to be concerned with. Let's say one-second pulses, about every minute-and-a-half. Duty cycle of 1 in 90, near to 1%. Took weeks, maybe months to drain the battery if the car wasn't driven. When the clock failed, those "pulses" of power became constant, duty cycle of 100%, and then the complaints started. Yes, people got pissed when you told them that you could install new battery, or new alternator, or both, but they were still going to have to fix the clock or they'd be right back where they were now.
We used to cut the wires on a lot of clocks because the cheapskate owner wouldn't pay for a proper repair.
Please note that I am NOT saying that you can't buy a defective replacement alternator, or that "rebuilt" or "new" alternators aren't made to a price-point and quality gets sacrificed. I'm saying that a LOT of "faulty" alternators--or starters--or batteries--or whatever--were fine before they were installed on a faulty vehicle,
where the Tech failed to do a proper, THOROUGH diagnosis.