This paper analyzes whether repealing net neutrality (NN) improves or decreases the capacity of a regulator to make internet service providers (ISPs) extend broadband coverage through universal service obligations (USOs). We model a two-sided market where a monopolistic ISP links content providers (CPs) to end users with a broadband network of a given bandwidth. A regulator determines whether to submit the ISP to NN or to allow it to supply paid priority (P) services to CPs. She can also impose a broadband USO to the ISP, i.e. she can mandate the broadband market coverage. We show that the greater is the network bandwidth, the more likely the repeal of net neutrality increases ISP profits and social welfare. Regulation can still be necessary, however, as there are bandwidth ranges for which the ISP would benefit from a repeal of NN while such a repeal is detrimental to society.