FedEx Ground already has the ability to massively undercut UPS, but instead chooses to nearly match UPS's rates in order to drive the profit for the entire FedEx corporation. Until FedEx can get costs under control elsewhere, this will not change. Regional carriers already undercut UPS, which is typically why the earn the business of places like Amazon for Super Saver shipping.
UPS is already aware of its cost disadvantage, which is why packaged services (including supply chain solutions & logistics) are driving the direction of the company. Regional carriers may be able to cheaply deliver packages, but the lack the ability to store, provide packaging, provide on-demand pick-ups with varying capacity, handle ARS, etc.