At shove-against-opponent’s-body distance, I would be VERY concerned about retaining control of the weapon. Placing a weapon against an opponent could cause an action which beats my reaction time, so, I am going to be keeping the weapon in a “High #2,” if at all possible. (My High #2 is what some instructors would call a “pec” or pectoral index.)
BTW, attending Shivworks ECQC, in 2005/2006, broke me of thinking that the “hip” position has any value, whatsoever, in weapon retention. Holding my weapon anywhere near my hip level is tantamount to asking that my weapon be snatched.
Firing from a High #2 has the added advantage of placing shots into more-important bits than an opponent’s guts.
So, yes, academically, a contact shot might well stop an opponent more decisively, but, realistically, if I am justified in using lethal force, and need to stop the threat ASAP, I am going to use that force when the barrel is aligned with the desired bullet path, rather than take any added time to effect a contact shot.