Alternators can have intermittant problems, so keep an eye on it.
Especially if you buy autozone alternators and batteries. [They have great return warranties, but it is not uncommon to find yourself using the warranty!]
You may have had many other issues - who knows, but it seems crazy to lose faith in the 6.0L and Ford's products specifically ...... based solely on a battery issue. That can happen w/ any engine make / model / etc.
[ TIMES 2 ]
I'd buy another Alternator, from another source, preferably a New one, not a Reman.
After that ? New Batteries would be next.
This Gremlin is not the 6.0, or Ford's fault... Not bashing AZ here but.. You Get What You Payed For... when it comes to Reman, and Store Brand parts & pieces ?
The ROI thing ?