I have noticed that AI troops seem to be wearing bulltproof vests.
For example: I had 3 rifle squads, 1 Platoon HQ, a machine gun team (at least one) and a mortar all attacking a single anti-tank team.
Not only did the enemy get off a couple of shots, but he got a couple of hits. AND... I didn't kill him.
So, forget suppression, clearly that doesn't work. How do you kill an enemy soldier IN THE OPEN?

I am sure you have noticed how an enemy squad will begin to run around in circles, or back and forth across lines of fire, and remain relatively unscathed for a couple of turns before finally being eliminated. In more than one instance, I have had single soldiers (Used up mortarmen, last member of a rifle team, or observers, or sharpshooters) draw fire away from intended targets to allow other AI troops to advanced without any resistance.

I'm just a novice at the games myself, so take what I say with a grain of salt.

One thing I didn't realize at first was that the men do not represent individual soldiers, since the CM games predate computers with the power to render that many units at once. Each man you see on screen is more like a game piece that represents about 4 actual men in battle. Clicking on a unit and hitting ENTER will give you the complete rundown of your forces, and as you take casualties individuals within the unit will be injured and/or killed without immediately changing the number of men you can see on the field.

This applies to enemy forces as well, so your guys may very well be dealing death and destruction numbers-wise without your seeing it visually. Depending on how high you've set the Fog-of-War, you will also receive no info on this until your men walk up on the dead bodies.

As far as suppression goes, it does work but there is a trick to doing it effectively: don't target the enemy unit itself directly with your suppressing force. Instead, I like to target the ground just a tiny bit behind the enemy (the command will change to "Area Fire"). Your boys will hurl the lead downrange like nobody's business and the bad guys will hit the dirt. Have a second unit ready to do a hook around their flank and you'll be home by Christmas.

As far as the AI, well, dumb AI plays games because smart AI is occupied with building SKYNET. From reading the Battlefront forums the consensus is that it is much better in defense than attack. The scenario designer may often suggest which side is better for the player in a mission. In its' heydey most players went head-to-head anyway.

I hope this has provided some help for you. These really are "Good Old Games" and a lot of fun. Try the suppression technique with Area Fire. The first time I made that work the neighbors knew about it as I cheered my grunts to victory.

The thing I love about this game is that it's possible to totally annihilate the opposing force if you take your time and move thoughtfully, with minimal casualties to your own troops. Every little thing you do counts for something.

I'm gonna hi-jack this thread to ask question about AI in this game, but before that - you can definitely kill units, it's just take so much time dunno if it's worth it. 2 Shermans had to use 3 phases and lots of shells to kill my HMG hiding in hedges [200m].

My questions about AI would be: does it cheat? I'm only 3 hours into it, played Tutorial mission [couple of times] on Axis side - cause I thought defense would be easier. NOPE. Can't beat it, Shermans always roll in, spot, shoot - never miss, and kill both PZ IV.
No matter how well I hide them, and I spot them first, Sherman will always shoot first, and always with penetration.
Did developers handicap Axis forces? Even when I sent some units on suicide mission to draw tank fire, and I could somehow kill both enemy tanks, Airborne Infantry always wins against my 44th.

AI definitely can make some dodgy plays, when it moves, shoots, rotates, reverses... all in the same phase.
So definitely something is off, either AI, or Axis units in tutorial are reservists, or I don't know. Old games I guess.

BTW: escape minimizes the game?! Really? Almost gave me heart attack first time I pressed it, 20 minutes of setting my units down the drain... what were they thinking?