PA powers can be quirky. I don't know about that particular advantage on Wrist Bolter as I've never used it, but it wouldn't surprise me that it doesn't play nice with other powers in the set.
I do know some of the other powers are misleading in what they are and how they work. Plasma Beam, for instance, is a maintain, but it's treated like a charge and not a toggle. So it doesn't work well with chargeable powers like Chest Beam or Tactical Missiles which also don't work well with each other within the theme of the set mechanics. Shoulder Launcher is really a tap AoE nuke with a long animation, but the animation acts like a toggle. Which is great for triggering Overdrive but can cause the actual attack to not fire properly if you're not careful.
One of my PA characters uses Eye Beams, Chest Beam, and Plasma Beam. I can use Eye Beams with either other power just fine, but not the other two powers together. I have another PA character that uses Mini Gun, Micro Munitions, and Tactical Missiles. I can use all three together in pretty much any combination until my blue bar runs out so long as I take care in charging Tactical Missiles.
As to whether or not some of the powers are properly treated as AoE or single target for things like Mass Destruction or Focused Strikes, though, I don't know as I've never personally tested that or even bothered to research it.