The rapid increase in computing demand and its corresponding energy consumption have focused attention on computing's impact on the climate and sustainability. Prior work proposes metrics that quantify computing's carbon footprint across several lifecycle phases, including its supply chain, operation, and end-of-life. Industry uses these metrics to optimize the carbon footprint of manufacturing hardware and running computing applications. Unfortunately, prior work on optimizing datacenters' carbon footprint often succumbs to the \emph{sunk cost fallacy} by considering embodied carbon emissions (a sunk cost) when making operational decisions (i.e., job scheduling and placement), which leads to operational decisions that do not always reduce the total carbon footprint. In this paper, we evaluate carbon-aware job scheduling and placement on a given set of servers for a number of carbon accounting metrics. Our analysis reveals state-of-the-art carbon accounting metrics that include embodied carbon emissions when making operational decisions can actually increase the total carbon footprint of executing a set of jobs. We study the factors that affect the added carbon cost of such suboptimal decision-making. We then use a real-world case study from a datacenter to demonstrate how the sunk carbon fallacy manifests itself in practice. Finally, we discuss the implications of our findings in better guiding effective carbon-aware scheduling in on-premise and cloud datacenters.