It’s illegal touching, which ends the play. There is no yardage penalty for illegal touching.
EDIT: Doh! That’ll teach me to leave thread tabs open for 20 minutes before replying. I should at very least preview first. heh.
No concrete cite, no. (Not sure how what to search for.)
But consider if it was just past a first down marker instead of the goal line. Where would they spot the ball in that instance? Where his feet went down, because that’s where he established possession.
Penalty! 
It’s always been my understanding that forward progress is marked at the position of the ball, not the man. That’s why runners will sometimes stick the ball out in front of them when running out of bounds or being tackled from behind.
I’m willing to accept there may be exceptions, but that is the default rule as I understand it (and I could certainly be wrong).
No Touching!
That’s for people who already have possession, which is a different rule. As stipulated earlier, for someone who already possesses the ball, the ball must break the plane.
The receiver doesn’t possess the ball until his feet come down. (Or any qualifying body part.) Once his feet (or whatever) come down, where they came down is the spot where the receiver has established possession.
There is no “forward progress” component to catching the ball, only to advancing it.
Fair enough.
Just seems it would be a lot simpler to mark it where the ball is in every case.
That would result in an awful lot of out-of-bounds incompletions when the receiver gets his feet in but the ball is outside the field of play. Imagine the replay nightmare trying to determine if any part of the ball were above the out-of-bounds sidelines during a catch.
Much simpler to just watch the feet and mark it at the feet.
I don’t care about out of bounds. I care about North-South.
If you don’t care about out of bounds, only North-South, and want only the ball to matter, plays like this would be ruled incomplete. That’s a pretty North-South play to my eyes.
I don’t know where you’re getting that from. Spot the ball where the ball is when he is down. But that’s not the point anyways. The point is, I believe shouldn’t be a touchdown if the ball never enters the end zone, all other scenarios notwithstanding.