The thing with esper chip skills (in terms of balance) is that they're like a weapon (red) or skill (the others) that doesn't take up any of the slots. That technically means your loadout is fundamentally stronger just by having access to the F slot (disregarding the stat boost).
What's more, they can be used on top of things like hp+/sp+ (you're even counting on that). It would have to be some kind of miniature "ult" with limited use cases, or just a small boost to your movement or something (but not in the same way as a normal skill in that case).
We would have to make something where people wouldn't just say "why isn't this just a normal skill?" Because if it changes how you play as much as with with shield or anchoring, then it's better off being a normal skill (unless maybe it's balanced enough around being an F skill).
So here's an idea:
A skill that roots you in place for 1-2 seconds and then heals teammates around you for 20 hp. It would have a 2 min cooldown (at least, 4 min might be better) and it would be 1-5 min longer for each healing weapon you have equipped.
That way, you could make a more agressive push towards the goal or turn a fight around, but if you're a dedicated healer it recharges slower. My gut feeling still says this might be unbalanced. Maybe it's even underpowered as you might just use a rescue gun instead, but it's better than a "kill button" (a railgun or revolver is supposed to take a weapon slot to use).
Lastly, a way to disable stats and esper chip skills would be cool. By adding more F skills the (meta)game might become more balanced around them, so it would be nice to have the option to disable them. Also maybe a normal skill in SO other than hp+/sp+ could spice things up a little maybe? Idk, I don't play it that much, but that would have to be for another thread anyways.