The recent provision of energy-harvesting capabilities to wireless sensor networks (WSN) has entailed the redefinition of design objectives. Specifically, the traditional goal of maximizing network lifetime has been replaced by optimizing network performance, namely delay and throughput. The present paper contributes to this reformulation by considering the routing problem for the class of time-driven energy-harvesting WSN (EH-WSN) under regular or quasi-periodic energy sources. In particular, this paper shows that the minimum hop count (MHC) criterion maximizes the average duty cycle that can be sustained by nodes in this type of scenarios. This is a primary objective in EH-WSN, since large duty cycles lead to enhanced performance. Based on a previous result, a general expression is first obtained that gives mathematical form to the relationship between duty cycle and traffic load for any node in a time-driven EH-WSN fed by a regular energy source. This expression reveals that the duty cycle achievable by a node decreases as its traffic load increases. Then, it is shown that MHC minimizes the average traffic load over the network, and thus it maximizes the average duty cycle of nodes. This result is numerically validated via simulation by comparison with other well-known routing strategies. Accordingly, this paper suggests assigning top priority to the MHC criterion in the development of routing protocols for time-driven EH-WSN under regular energy sources.