As a previous dairy farmer, cows are measured by lbs per milking not gallons. Equating 8lb/gal, and the 3x per day you mentioned this would be extremely average to low producing cows and they could NOT milk for 3 years, they would go dry on their own. Come again?
Maybe it was 3 gallons per milking. But I do remember what they told me about the milk production time being 3years after the year the calved. Of course, I was just taking the tour; maybe they lied to me.
My personal diary experience was at an old school diary with grazing/hay fed cows that were hand milked until a small entry level milking machine was acquired. Never more than 100 head.