In the Mobile battles that you'll see with online players, I find that LAVs are a highly important front line. The fact that they take up a space can be used to regulate the flow of the enemy. Use your LAVs to plug up holes so your enemy can't sneak by with transports to hit your artillery, etc. Even if they are dying by the droves, the fact that the enemy can't move over them until the next round keeps them vital.
And when you're fighting a holding action, nothing bogs the enemy down more than having to try to smash a hoard of those annoying units. A couple extra turns that you can hold off an enemy can make the game, as you try to get reinforcements in time.
Of course, these same traits make LAV's tough to use in a running battle. They get in the way of your faster units, and like Vic said, can cause a major traffic jam.
Speed is essential in this game. You have to be ready to use any slack you can get to move the battle line farther. I learned this when I got badly beat by Tiger
. LAVs can prevent an enemy from doing this better than any other unit. Sure, a line of Heavy Bots is impressive, but they are a very expensive unit that takes only one hex. The enemy will get around, isolate, and destroy your bots, while taking out your not-very-well protected artillery.