Digital Twins (DTs) are digital representations of physical objects or processes that can be used for their computer-based analysis. This technique has been used in different fields to analyze, simulate, and optimize various scenarios in real time without interfering with the real twin. Using Serverless Computing as a use case, this paper discusses the underlying costs of using DTs when applied to analyze and optimize the management of computational resources for cloud-continuum applications. We argue that, although feasible, using DTs for Digital Systems can be prohibitively expensive. Defining the ideal DT fidelity for a given application is challenging, as this impacts both system management and performance through heavy monitoring as well as the DT running costs.