"Great. Now I can flatten light ammo against body armor faster than ever before."
Honestly, while over the four 'runs I was in at DragonCon I shot only ... two rounds (AV vs. armored window) and one (Gamma-Scop against that technomancer), unless your character is a serious hard-ass and has seen a lot of combat, realistically they're going to be shooting back -- a lot. Even if they hit, they won't know/realize it right away, and squeeze off another three or four rounds, just because it takes a moment for a body to slump to the floor. Plus, accuracy (even with a 6 in whatever, smartlink, etc. etc.) is going to suck, because of sheer 'they're trying to KILL me!!!' twitchiness. The targets (read: security / gangers) are going to take cover and shoot back, not stand in the open like Imperial Stormtroopers.
Unless the character has that whole SpecForces / Merc / High-level bodyguard background (because high-end bodyguards are trained in live-fire or near-live-fire conditions to react properly, i.e. get their principal the hell out of Dodge City) / Agent background, they should probably be wasting at least a clip of ammo per fire-fight. Panic fire, inaccuracy, 'make sure he stays down' ...
Hm. You know, I just thought of a way for that rule to play out. Starting firearm combat dice pools -- because hand-to-hand is different -- would be something like 1/3 to 1/2 their trained size, due to an unfamiliarity with actual combat. Not sure how to define exactly what that should be, but I'd adjust it to the character background anyhow. For each combat full-Turn-or-longer combat the character is in, 1 die is returned to the skill pool, until they're at full -- at which point their combat experience is at the same level as their combat training.