I don't know but I assumed those skills were meant to be paired with things like that accessory that makes your normal attack hit 8 times or something. Seems like a meme to me even if you do build around it and I think usually it would probably be used when your character is countering with their normal attack but other than that you're probably not meant to be using it as a main source of damage. I guess it could also make it more useful if you need to normal attack or defend to regain sp but it feels kind of redundant.
Counter seems a mechanic that sounds great on paper, but hard to take advantage of in practice
Ai often ignores your counterer even if you give them "gets targeted twice as much" item (and this item has to compete the same equipment slot with the actual counter chance, which at this point the highest I've seen is counter rate 46%) - basically in my testing I almost never triggered it - consider all these complications against something like double bite, that kills everything I encountered so far with the exception of Mimics that just kill my fighter with kajillion untyped damage on turn 1
You can consider ~solo-playing with only your "counter specialist", but it seems to not ideal, considering presence of insta-kill moves and various nasty status effects(that you can't necessarily always easily resist, which tells me that game is more geared toward playing with full party that can revive\cure status effects)
Anyway, I think if you can trigger status effects from aoe skills (which was first things I thought of when I saw "innate strike effects") it's be much more useful (and useable) than having any use from counters. Say, you have the the garbage-tier on hit paralysis effect chance 10%. If you hit 4 enemies with it (and if I remember how probability theory works and provided that have no resistance to it) you get smth like 40% chance it paralyzes at least one guy, which is pretty great, I think (and consider that you often have more than one strike effect all of which can trigger independent of each other)
Check the detailed info of the skills(A-key). Most skills have something next to adds status. Also most enemies have status resistances.
Oh wow - I had no idea about this button, thanks for the hint. I'm unsure whether it reflect the innate strike effect application or not though
Edit: it seems like it does