Why do most h bridge modules have more leads than 2 inputs, 2 outputs, and 2 for power?
There are two functions that these "redundant" pins provide. Using your first datasheet as a reference, the grouping of pins helps to show their function.



Groups (9,10) (13,14) (15,16) and (11,12) are tied together to reduce resistance and inductance. 

The pins directly connected to the source of each transistor (1,3,6,8) are lower resistance, lower inductance connections to the sources which is better for the gate drive circuit. Keep in mind that some gate drivers can drive over 9A peak gate current, so minimizing inductance is a must.

In terms of tying control pins together, that isn't possible with power devices due to dead time switching requirements and gate drive voltages.