This image is from the AMC Story Sync, for reference.



I don't think they'd kill everyone. My understanding was just that they'd just kill people in the areas around the SZ, like an additional perimeter of sorts. They're still "gearing up to retake the city" so I doubt their purge has been as effective as you think. Even if it were, it'd be very counter-productive.

 

There are 18 MILLION people in the L.A. area. There's no way the army could kill even a decent number of them before people figured out what was going on and went berserk and overran the military. Look at the area of where these Maddie and Travis live, it's not in downtown somewhere, or a place with a high population density, it's relatively sparsely populated. This makes it a good place to put up a couple of layers of barricade and isolate it from the rest of the city, either to protect it, or if you're feeling paranoid, to have it act as a contained test zone for some evil experiment.

And remember, this is all occurring in the initial days after the outbreak, where these aren't being called zombies but "the infected". Even it the central command wanted to kill everyone and had the means to do it, would U.S. soldiers really be willing to sterilize Los Angeles when ordered to? This is supposed to be happening NOW, so if you answer yes, you really believe that the military is willing to sterilize L.A. now.

 

You are right except that this is supposed to be happening in 2010 I think?

It is also happening EVERYWHERE at the same time.
The Military is not that big and as you so rightly state they are not just going to kill everyone on an order to do so.
They all have families too and many or most would likely go A.W.O.L. I would think to be with family by now.

Also if the Military wanted to "Sterilize" L.A. why wouldn't just letting this thing run its course be the simplest way?

 

Controlled Burn

It seems to me that there are three classes of civilians at this point: those who bugged out, those who sheltered in place until moved to a safe zone, and those who refused to be moved. The first two do not much concern the military's current operation, it's that third class of folks who refuse to come under the protection of the military but also insist in sitting just outside their gates. Each of those folks is just a loaded weapon, ready to be fired at the safe-zone. They get bit, they get the fever, they drop from a heart-attack, whatever and instantly they are hurtling towards the safe-zone. Killing these recalcitrant folks is kind of like doing a controlled burn to create a fire-break around their camp. That's the only sense I can make of it.