It is hard to pin Kearny down. A hard fighter yes but never found an order he didn't question. Chain of command only up to a point. Reach a high point as Brigade commander but never had the chance to demonstrate his ability above that. If he survived he most likely would have either got the I Corps command or the III Corps. Both would have given him an opportunity to show he could handle a larger command.
I would honestly be actively
surprised if Kearny turned out to be able to handle a larger command - his decisions when actually in command of his decision show that he struggled with battlefield handling of his division. He makes an actual
habit of ordering disjointed charges that disrupt the battle line (Williamsburg, Seven Pines) and sending for/trying to command units from a different division instead of running his own (Glendale*, Second Bull Run, Chantilly).
The fact he's doing this literally right up to his death (his last action in his life is to order a poorly conceived charge from a unit of a completely different corps) makes it a hard road to row to argue that he'd somehow improved or was somehow maturing. By Chantilly he has been substantially involved in five major actions and in none of them has he really displayed division-level management skills; if he got a corps by seniority, which might well happen, I doubt he'd suddenly change his established patterns of command.
* as an aside, I find it funny that - per Grubbs - Kearny calls for the 1st NJ bde, no longer his, to do something, but (I think a bit earlier) Kearny's own reserve bde had been asked for to prevent the battery being lost in the first place and that reserve bde refused to move without Kearny's approval, and he couldn't be found to approve it.
Bringing the