Limit the usage of powers to only once per battle?
I don't think that it would help much, unless this also includes mechadendrites and claws, and even then, it would just promote having more of them. I think these are some of the main issues:
Health regeneration is far too abundant. I'm currently rolling with curatio claws and healing mechadendrites on every non-frontline techpriest; my frontline guy still carries a curatio claw. Whatever damage the enemy inflicts is easily healed up. It's an iffy line to walk though because if you don't heal promptly, you'll probably lose your guy pretty fast, so maybe it's largely a product of having lots of healing and low health pools. Might be fixed by making your units be somewhat tougher and having more health, but healing abilities drastically reduced, so you wouldn't be in danger of dying in a couple turns of not healed, but at the same time if you repeatedly let your guys get hurt, they will die, and if you're sloppy you will still get worn down through the mission. As it is, not only is it easy to keep my guys at full health, but I actually spend most of the time with two or three healing devices available and nobody to use them on.
Cognition points are an interesting mechanic, but too powerful. On the one hand any weapon that's not a peashooter (and peashooters start to become useless midway through the game) consumes lots of cognition points. So you build to be able to use it. The recover-all-CP skull upgrade, scanners, the fill-CP-bar ability, the weapon cost reduction ability, etc. Now you're at the point where you can use your weapons most of the time and deal with CP costs, but if you have to have a dude run around and go anywhere on the map, you can do that, because the relative CP costs of movement are low. I would lean towards making CP harder to get, but reducing weapon CP costs. Or make CP harder to get, keep weapon CP costs the same, but make the high CP cost weapons stronger.
The arc weapon you get for whatever-edition is really powerful. You can use it on a melee guy and retain your bonus and absolutely destroy anything in melee. But that makes me think of a broader issue: by and large, your guys can do anything. My main gun dudes haven't even maxed the dominus tree, I maxed out Lexmechanic instead to pay for weapon costs. And dipped Explorator for them so they can ignore attack of opportunity. And dipped all kinds of other stuff to get the best equipment and so on. My Secutor has no weapons, he has a Cog Occultaris and stays untargetable the entire match and is loaded to the brim with healing gear so he just runs around standing near large CP points, healing troops, and buffing troops while being invincible. (I haven't tried Tech-Auxilium yet but I suspect its finisher ability is actually even more broken than Lexmechanic since it'd let you mostly-fill CP every couple turns instead of totally-fill CP every five turns). And that makes me think, you know... maybe classes should have been more rigid and nonflexible. Maybe you should have had to pick one, or MAYBE two classes, per techpriest, and you can only level up those. So your ranged guys can't each be able to max out the CP bar and run past melee enemies with impunity, for example. And restrict gear. Healing stuff for Enginseer only. Heavy ranged stuff for Dominus. Xenarite weapons for Xenarite. Melee for Secutor. Maybe exotic weapons for Auxilium. And a couple basics that everyone can use. Etc. I haven't checked custom difficulty settings so maybe there are some class restriction options already available, probably helps if so.
But I feel like overall, having each techpriest have specific roles and not being able to turn them into generic do-everything guys or cherrypick broken combinations would help with balance a lot, and maybe make gameplay more interesting. Sure, it'd reduce customization, but I think it would enhance the actual gameplay, including gameplay elements that are there already like attacks of opportunity, that contribute a lot to having a more active feeling battlefield where you have to be careful of what's going on, and then get bypassed by "lol I dipped Explorator I can escape melee at no cost".
I dunno, the game is way too easy to break. I think after my current playthrough I'm going to try a Troops focused game using only one or two techpriests (ie, the ones I start out with) and the rest of my team being Troops only. I suspect it'll still be pretty broken but maybe it'll make things more interesting.
Edit: actually I think the most OP build would be a team of Tech-Auxiliums spamming that machine spirit canticle to use boosted damage, no CP cost arc weapons every single turn. I haven't tried this yet but I will at some point.
Edit 2: having acquired another techpriest in my current playthrough I decided to set him up as Tech-Auxilium. The extra canticles thing didn't really blow my hair back, but I haven't tried a whole squad of them. Moreover, I haven't thought much about what sort of canticles might go from mediocre to broken when able to use them repeatedly.
More significantly I tried out having multiple Sector techpriests with a skitarii gunline (4 or 5 skitarii, preferably high level Vanguard). It is very powerful. Each time you fire off the "all troops attack this target", if you've placed your troops carefully, whatever you targeted will usually die. If you have three or four techpriests with that skill, and a bunch of Vanguards, that's a lot of damage you're dishing out in addition to their base damage (which is also substantial in numbers). So I do think I'll be thinking about the possibilities of generally ignoring Tech-priest weaponry and maxing out their ability to support and boost troops.