When competition is reduced, loyalty matters less to the remaining airlines. Why should they invest in rewarding traffic that is going to turn up anyway? That thinking will stick until the next major recession.
And if AA continues to outperform UA and siphon HVF traffic from UA I can't imagine why they would want to emulate UA with a revenue-based FF plan that is already pushing former UA loyalists into the reconsideration / Kayak pool.
DL can do it because they run the best airline. UA, not so much. If AA resists it could make UA the long-term number-four carrier in the US.