So if as I rotate on takeoff, the Stall warner erroneously sounds, the THS drives the aircraft into the ground
I was just putting the logical result of Ian W's suggestion into words as it is an interesting idea and I try to keep an open mind -- but I don't think the solution is more automation, hence why I put "controversially" and why I ended how I did.
I won't get into a fight, since you drive A320s and I don't, but
AFAIK existing stick pusher logic includes an altitude minimum (e.g. Q400 only activates > 200 feet AGL), so there's no reason you would not implement equivalent logic *if* you were to do this.