Vehicles are very different. You seemed to be only referring to infantry above, as I was, so I was only talking about them.

There was both cooldown and ammo weapons in both games, and I think it was consistent between them.

For starters, vehicles are extremely limited in mobility and any exploitation is generally met with the vehicle exploding or the player getting kicked out. They are far less versatile, and are far more difficult to exploit when two game systems collide. The shooting mechanic on foot is already far more complex because not only can the player change the equipped weapon in many cases, but infantry in general are far more versatile. They have the ability to constantly change states, enter things like canons and vehicles, and move freely around the environment. This not only leaves a massive gap for exploitation, but it also causes developmental issues. Let's look at the code.

The Droideka and the Super Battle Droid are their own character type, (when unpacked "ctSBD" and "ctDD"), and have different bone structures and state machines. Weapons and abilities are not synonymous between these and the rest of the characters, most of which conform to the standard type which appears to be based off the standard Rebel Soldier.

Both of these characters are more limited in their abilities than the rest. They act more like vehicles than characters in how much they can do. Pistols share the same "cooldown" that vehicles have. It's the standard system (scrapped from the second game in favor of the more complex universal system). The pistols, because of how weak they are, wouldn't make a difference even if a player found a way to bypass the cooldown, which isn't hard because every time a new state is taken it resets, as does everything else besides ammo and health, which are always stored. In the second game the weapon cooldown is stored as well, along with a few other things.