I think the market for Global Entry reimbursements is approaching saturation. This would be a "me too" benefit, which probably no longer costs much to offer, but isn't likely to sway people who are otherwise undecided about a new card.
I think Chase is too invested in hotel partner cards to undermine it with a benefit which undercuts the prices available to Hyatt, IHG, Marriott/Ritz cardholders. (I also think Chase's relationship with three direct competitors is unsustainable, and they they will lose one, but that's another thread.)
I agree on undermining existing relationships as well as four relationships not sustainable (including Fairmont), doesn't Amex Plat give you SPG Gold status with Platinum but not with Amex SPG card?