You won't get higher output unless something is demanding current to satisfy need. IOW, the ABILITY to produce more output doesn't mean that the higher output is produced unless something calls for it..... it could be that the battery has an internal short - get it checked at a reputable shop.
If your voltage regulator allowed the alternator to pump 16v into the battery, there's a chance the battery is damaged.
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The alternator doesn't stop spinning. When the resistance of the battery or curent draw on the system goes low, the regulator pegs the o/p voltage at some determined max level. If that is exceeded, it implies the regulator is not functioning correctly, not that something has called for more power. If there were a significant unexpected current draw, the voltage would in fact drop.
All the quoted o/p numbers (ability) are reman bench tests. I'm assuming they use the same load, rpm etc... so the comparisons are valid.
You point on the battery is correct though. It could be failing under mechnical (vibration) stress that would never be apparent or indicated by simple cold start peformance and a healthy 12.8V on the multimeter. Thats rare in my experience, but then, so is replacing an alternator 4 times..... It could also be low on fluid having been exposed to >16V.
Point is still that a stock Alt rebuild shouldn't be significantly better than stock. If it was designed or rebuilt to do so, OK. It's possible the rebuild company is doing something legit but odd, like building all 90-xxxA mitsu units to meet xxxA spec, but then why did the most recent unit only show 100A?
Paul