In October 2015, the European parliament has decided to forbid roaming charges among UE mobile phone users, starting June 2017, as a first step toward the unification of the European digital market. In this paper, we aim at investigating the consequences of such a measure from an economic perspective. In particular, we analyze the effect of the willingness-to-pay heterogeneity among users (also due to wealth heterogeneity), and the fact that the roaming behavior is positively correlated with wealth. Considering a monopolistic operator, we compare the paid-roaming situation (with usage-based pricing) to the envisioned free-roaming from the point of view of the operator and of users. Our analysis suggests that imposing free roaming degrades the revenues of the operator but can also deter some users from subscribing. This is because paid roaming allows some partial market segmentation; hence we conclude that such (apparently beneficial) regulatory decisions must be taken with care.