Assessing the energy consumption or carbon footprint of data distribution of video streaming services is usually carried out through energy or carbon intensity figures (in Wh or gCO2e per GB). In this paper, we first review the reasons why such approaches are likely to lead to misunderstandings and potentially to erroneous conclusions. To overcome those shortcomings, we propose a new methodology whose key idea is to consider a video streaming usage at the whole scale of a territory, and evaluate the impact of this usage on the network infrastructure. At the core of our methodology is a parametric model of a simplified network and Content Delivery Network (CDN) infrastructure, which is automatically scaled according to peak usage needs. This allows us to compare the power consumption of this infrastructure under different scenarios, ranging from a sober baseline to a generalized use of high bitrate videos. Our results show that classical efficiency indicators do not reflect the power consumption increase of more intensive Internet usage, and might even lead to misleading conclusions.