There are two possible states of consideration:
1) Shadowrun is an Action Adventure Game
2) Shadowrun is not an Action Adventure Game
If shadowrun is an AA game. It is lacking. The game does not offer meaningful tactical choices as well as similar games (Savage Worlds and d20).
If shadowrun is not an AA game, well it does not have the mechanics to make it otherwise.
Sophistically, Shadowrun is nWoD.
Now, I'm AFB (at least AFSR4B) right now, so I couldn't tell you if this is in the book, but I suspect it is. Every single Shadowrun game I've ever played has been immensely tactical, but not in combat. What does that mean? It means that Shadowrun works a lot like a TV episode: there's a set format that most adventures take. That format looks like this.
Get lead on job <--------
| |
V |
Negotiate with Johnson--
|
V
Legwork (Gathering info on target/setting/employer/whoever) <----
| |
V |
Develop plan of action-------------------------------------------
|
V
Actually go on run------------------------------------------------
| |
V V
Complete run Get double-crossed
| |
| V
| Kill that rat bastard Johnson
| |
V |
Collect money <--------------------------------------------------
The planning stage can (and usually is) immensely tactical, to the point of absolute absurdity. I am reminded of one time where the DM had surrounded a building with about thirty people, and we were supposed to help those inside the building out. We were SUPPOSED to cause a distraction or something; I don't know. We ended up planning an assault for literally an hour, during which time the GM's face kept sinking deeper and deeper into his hands. When we implemented said assault, the GM just looked at our die rolls and started wiping off about five people at a time.
None of this was done with houserules of any kind.
So I reject your notion that Shadowrun isn't tactical at all; it is most definitely so on a long-term scale. So let's examine a short-term scale.
First, have you read the expanded combat rules in Arsenal? I disagree with your assertion about the simplicity of the core rules, which I'll get to later, but leaving that aside have you ever seen them? They add a lot of complexity to combat, if you want it there.
I can't argue about the exact number of options in combat as I'm AFB, but I will say this: the reason that you see a lot of shooting in SR4 is that shooting is pretty much the optimal thing to do. And that is not a bad thing. I can't really argue about the number of tactical options, but I can argue about tactics themselves.
I utterly reject the notion that SR4 has to be tactical to be a good action-adventure game.SR4 has a lot of sneaking, that's true. But it's also a very beer-and-pretzels, fast-paced "hack-n-slash." In fact, I would argue that Shadowrun is the first-person shooter of RPGs: it's fast, furious, has a high body count, and a higher explosion count. (Also, it's a good setting to have lots of flaming barrels, but the PnP version doesn't have a graphics engine to show off so they're kind of pointless.) SR missions aren't designed about pulling off the perfectly-planned caper; they're about making absurd plans and then having to blast your way out anyway when shit goes wrong. And that, to a lot of us, is fun.
I freely admit that it is not the wargame descendant that D&D is. But if you want to show that an AA game has to be tactical to be good, you have a long way to go.