I don't think, knowing the turn order would help.
You can easily get yanfly's turn order display plugin, tweak it a bit to fit in the game. I've tested it and it did not change anything. I know who's turn it is and may decide to defend, but my agility doesn't quite change as frequently to change my position. I'll roughly be at the same place next turn... At some point, you kinda ignore that turn order and attack to make some progress... The only slight benefit you get out of it is to know which enemies to focus on to prevent some of their turns if there's no overblown protection, and you're sure to one shot them to be a little bit more efficient...overall however not much of a difference that blows your socks away like it appears to be.
Knowing the Turn order does absolutely nothing if you don't know what action they make!
I don't know how that plugin works, but what I was thinking was something along the lines of the old Final Fantasy 10 turn order display, which shows the turn order for up to several turns, and gives a preview of what changes will take place before you lock in your turn. Say Karryn would be first in the turn order next turn, then you choose, I dunno, Cleave. When you highlight Cleave, the game shows you that if you select Cleave, Karryn's turn will be knocked down to third next turn. Stuff like that would be incredibly helpful whether you know what the enemies are going to do or not.
As for knowing what action the enemies take, it's not an exact science, but you can absolutely predict their actions to a limited degree just based off of their portraits. If a character is in a neutral state, they're going to be more unpredictable. If they're blushing (aroused), then they're very likely to try to grope, strip, or fuck Karryn. If they're pissed off, they're pretty much guaranteed to attack her. Combine this information with a few fairly easy to obtain abilities like Taunt and Cock Stare, you can pretty easily manipulate enemy actions with the barest amount of luck. The problem being that without knowing the turn order, it's difficult to actually capitalize on that, so there's not much point. Your best bet in most fights kinda feels like "just kill them before they can cause problems" for most casual players, so I definitely agree with you on that point at least.
The game really has a lot of mechanics that it doesn't explain, but not all are equally impactful. Most are just smoke and mirrors.
I'd imagine that probably is the case, but I couldn't say because the game obfuscates the mechanics, so I have no idea what is or isn't important because I don't even know what the mechanics DO. If they were adequately explained, then I could probably just agree with you here, but since I don't know what mechanics do what and how or why they do it, I can neither agree nor disagree because I don't have enough info. If I knew what the turn order was, and it still didn't help the combat feel any less like a crapshoot, then I would agree that it doesn't matter. As it stands I would prefer to have that info than not, because that's just one less thing making the game obtuse.