Not having exchanging attacks is an interesting choice. It favors the side with more units, but it'll only really be an overwhelming advantage with a supremely competent commander calling the shots. If the enemy units had advanced when we first encountered them and focus fired on the Operators, then we could have been in a lot of trouble.
Operators being the only ones who can double is a solid design choice. It puts them into the glass cannon slot pretty nicely. Otherwise they wouldn't really have anything to make their squishiness worth it.
I'm slightly eh about the current equipment weight system. It makes sense and prevents people from having a weapon for every situation as well as health items, but if a support unit wants to be able to heal, repair, and have a second weapon just in case, they're going to be in a slightly rough spot. The solution of course is to actually play the support unit as support rather than trying to set up an evasive glass cannon build, or just commit to the glass cannon build and drop a support item. Or one could bring along a vehicle to store healing items and exchange them around as needed, but that's not entirely in the spirit of covert ops and time limited operations.
Basically, the equipment system works the way it was likely designed to and I'm just nostalgic for being able to carry 5 weapons and 5 items at once with no consequences.
An item that's able to provide vision like the battle scanner ala New XCOM would be useful, though figuring out sight lines and all that could be a headache.
Removing damage increasing stats and damage reduction stats is an interesting choice as is having flat health (if my memory is correct anyway). For Operators, it really makes the choice of being able to hit well, evade well, or a mix of both, a tough decision. One bad turn and you can be full of regret for not specializing the other way. But that's true of most games in this format so I'm basically making idle commentary.
I feel like healing is at just about the right spot. Combat can be rather lethal, but if your guys survive you can patch up most if not all of the damage and keep your guys in the action. The low QL for the higher level heals also makes you want to wait for just the right moment to use it in case there's more damage coming in.
Maybe changing the Support class's special to healing items have .5 weight rounded up or are able to carry one healing item as if it had 0 weight would help with being stingy with healing if that ends up being something that you don't want. With the latter, they could have one weapon and carry three healing items (First Aid Kit, Surgery Kit, Repair Kit or Higher Level Repair Kit) before weight becomes a factor. I can see either system being exploited for more effective weapon capacity however.