High-dimensional systems are an important frontier for photonic quantum correlation experiments. These correlation tests commonly prescribe measurements with many possible outcomes but they are often implemented through many individual binary-outcome measurements that use only a single-detector. Here, we discuss how this binarization procedure for multioutcome measurements can open a loophole, unless specific device-characterization assumptions are satisfied. We highlight that correlation tests designed for multioutcome measurements can be trivialized in binarized implementations and we then show how to accurately analyze binarized data to reveal their quantum features. For seminal types of correlation experiments, such as Bell inequality tests, steering tests and prepare-and-measure experiments, we find that binarization may incur a sizable cost in the magnitude of quantum advantages. This emphasizes the importance of both accurate data analysis and implementing genuinely multioutcome measurements in high-dimensional correlation experiments.