Svennemir, When I played the AI I thought as you did.
If you want to kill AIs efficiently, just use infantry and ATGs at any non-open objective area of the map. The AI will run its vehicles into them blindly and die, and will be easily defeated (if no good close assault weapons exist at the time, tanks may be necessary though). Then you can take the rest of the map. But playing the AI is extremely boring since it does this each and every time (in generated battles, that is).
I've played quite a few PBEM/hotseat games, and my observations are that tanks and ESPECIALLY infantry are both necessary in order to fight efficiently, of course depending on the map. When I said that tanks dominated almost every battlefield in SPWAW, I merely meant that the amount of tanks was disproportionate to that of infantry, compared to real combat where tanks appear much more rarely. In my first PBEM games I relied solely on foot infantry most of the time, tanks appearing only late during surprise pincers movements when the opponent did not expect to find them. Still, they were necessary in the sense that the infantry wouldn't be able to catch the enemy tanks on retreat.
Now I'm already off the subject, but one favourite tactic of mine is to let a thin line of infantry advance, such that the enemy will have to engage them in close combat to pass. If the enemy chooses to attack the line hoping to break through at some point, I quickly mass armour behind a forest or hill nearby, then strike at a moment when many opposing vehicles are engaged in fight with the infantry, or are (unwisely) advancing past the infantry. At this moment, artillery will hit the enemy forces and a large amount of fast tanks, preferably loaded with infantry, will overrun the locally outnumbered enemies.
Concentration of force is the key here. Stealth, too - the enemy must not know what will happen. Of course the enemy can easily claim the middle objectives, but the infantry will reach them in time to force the enemy to act at some point.