The Wright catapult was powered by a 635 kg weight, dropped 5 meters.
It's potential energy, before dropping, mgh = 635 kg × 9.8 m/s^2 × 5 meters = 31115 Joules.
The 408 kg Flyer II was connected to the drop weight with a compound pulley that moved it 15 meters when the weight dropped 5 meters.
Dropping the weight converted potential energy to kinetic energy as follows:
mgh × 2 = drop weight mass (v)^2 + launch mass (3v)^2
drop weight speed = v
launch speed = 3v
The minimum flying speed was around 30 mph or 14.2 m/s
The catapult was mathematically evaluated with various launch masses, without friction or drag factors, using no gearing and 3x gearing for comparison:
Although the 1:3 gearing was a significant improvement in the catapult design, the 408 kg Flyer II was too heavy to reach launch speed, with a theoretical 11.4 m/s.
The much improved Flyer III, coming in at a svelte 323 kg, would come closer at 12.6 m/s.
Still too slow, with obvious solutions utilizing increased drop height, more drop weight, and still lighter aircraft design, why would the the Wrights hold below launch speed?
The answer may be in the other aspect of their development, the internal combustion engine. Holding catapult launch speed down may have given them a crucial abort option, with the plane dropping to the ground a few feet from the rails with little or no damage.
With a more reliable engine, a more powerful catapult may have been more desirable.
With sufficient runway length, it is not needed.