As for Centaur class having just 16 ships built... depends on what the class was designed for. It’s an older class (kitbash?) it seems that dates back to the 23rd century.
Its design and 4XXXX registry number connote a ship built during the ‘Lost Years’ between TUC and pre-TNG…probably more toward the latter than the former, since 5XXXX registries tend to connote Galaxy class precursors such as the Kyushu, Challenger, Springfield and Freedom. Up until about the 2340’s, Starfleet was still using predominantly older designs such as the Miranda, Excelsior (and variants thereof such as the Centaur, Curry and Raging Queen), and the newest class at the time was the Ambassador.