You just made a contradiction. If Jean is exhausting her powers to keep him alive, why would she have enough to be able to fly? She is either exhausted or she isn’t.
I personally have no problem with her being saved. Jean can’t do everything and has saved him her own fair share of times to earn moments of weakness. It is what makes her human.
What I personally am not a fan of is how Wolverine comes out of it? I recognize a high stakes moment can be great, but I think some more emotional would have fit better instead. Maybe Jean inadvertently projecting her pain becomes something he notices or something like that.