The transport sector is one of the leading contributors of anthropogenic climate change. Particularly, internal combustion engine (ICE) dominancy coupled with heavy private motor vehicle dependency are among the main issues that need to be addressed immediately to mitigate climate change and to avoid consequential catastrophes. As a potential solution to this issue, electric vehicle (EV) technology has been put forward and is expected to replace a sizable portion of ICE vehicles in the coming decades. Provided that the source of electricity is renewable energy resources, it is expected that the wider uptake of EVs will positively contribute to the efforts in climate change mitigation. Nonetheless, wider EV uptake also comes with important issues that could challenge urban power systems. This perspective paper advocates system-level thinking to pinpoint and address the undesired externalities of EVs on our power grids. Given that it is possible to mobilize EV batteries to act as a source of mobile-energy supporting the power grid and the paper coins, and conceptualize a novel concept of Mobile-Energy-as-a-Service (MEaaS) for system-wide integration of energy, transport, and urban infrastructures for sustainable electromobility in cities. The results of this perspective include a discussion around the issues of measuring optimal real-time power grid operability for MEaaS, transport, power, and urban engineering aspects of MEaaS, flexible incentive-based price mechanisms for MEaaS, gauging the public acceptability of MEaaS based on its desired attributes, and directions for prospective research.