Because a shotguns bullet spread actually isn't that huge for starters. Plus they're mainly short-range weapons giving the agents ample time to unload from a distance. Plus they're large and easy to spot as well as a bit cumbersome within tight spaces (a common place seeing as a lot of battles take place in city-scapes). Take note of the weapons that Neo and Trinity took with them in the first movie. Mostly small arms that can be easily concealed and maneuvered within tight spaces.

Of course in other environments they become more viable, but we see agents bend at large angles highly suggesting that even a close-range blast would be more up to luck than anything given an optimal spread. Plus agent reaction times are insane; especially given their machine status. Even an ambush sniper shot could be easily dodged by them. Finally, even if they did get lucky and scored a kill it would only be minor as getting a new agent in would be super easy. In other words, it makes more sense to try and focus on weapons that can deter an agent and slow them down while you escape than on actually killing them. The narrow passages that we see in the movies don't stack up well to the long barrels of shotguns and it makes much more sense to get submachine guns and pistols which you can easily hide on your person than a shotgun.

Not saying there isn't a place for higher power; just that the movies don't take place in such locations.

Also remember that they couldn't possibly win a war against the agents. Even a 100 to 1 kill ratio in favor of the rebels would be a victory for the agents given that they can easily build and program more while humans are highly strapped for numbers. Had Smith not gone rogue and changed the set-up there would have been no way Zion could have survived regardless of what they did.
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I am the gentle hand who heals, the happy smile who shields, and the foot that will kick your ***! - White Mage

Why did the rebels in the Matrix never use shotguns?

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