Instrumental systematics need to be controlled to high precision for upcoming Cosmic Microwave Background (CMB) experiments. The level of contamination caused by these systematics is often linked to the scan strategy, and scan strategies for satellite experiments can significantly mitigate these systematics. However, no detailed study has been performed for ground-based experiments. Here we show that under the assumption of constant elevation scans (CESs), the ability of the scan strategy to mitigate these systematics is strongly limited, irrespective of the detailed structure of the scan strategy. We calculate typical values and maps of the quantities coupling the scan to the systematics, and show how these quantities vary with the choice of observing elevations. These values and maps can be used to calculate and forecast the magnitude of different instrumental systematics without requiring detailed scan strategy simulations. As a reference point, we show that inclusion of even a single boresight rotation angle significantly improves over sky rotation alone for mitigating these systematics. A standard metric for evaluating cross-linking is related to one of the parameters studied in this work, so a corollary of our work is that the cross-linking will suffer from the same CES limitations and therefore upcoming CMB surveys will unavoidably have poorly cross-linked regions if they use CESs, regardless of detailed scheduling choices. Our results are also relevant for non-CMB surveys that perform constant elevation scans and may have scan-coupled systematics, such as intensity mapping surveys.