Electrocardiogram (ECG) reconstruction from contact photoplethysmogram (PPG) would be transformative for cardiac monitoring. We investigated the fundamental and practical feasibility of such reconstruction by first replicating pioneering work in the field, with the aim of assessing the methods and evaluation metrics used. We then expanded existing research by investigating different cycle segmentation methods and different evaluation scenarios to robustly verify both fundamental feasibility, as well as practical potential. We found that reconstruction using the discrete cosine transform (DCT) and a linear ridge regression model shows good results when PPG and ECG cycles are semantically aligned-the ECG R peak and PPG systolic peak are aligned-before training the model. Such reconstruction can be useful from a morphological perspective, but loses important physiological information (precise R peak location) due to cycle alignment. We also found better performance when personalization was used in training, while a general model in a leave-one-subject-out evaluation performed poorly, showing that a general mapping between PPG and ECG is difficult to derive. While such reconstruction is valuable, as the ECG contains more fine-grained information about the cardiac activity as well as offers a different modality (electrical signal) compared to the PPG (optical signal), our findings show that the usefulness of such reconstruction depends on the application, with a trade-off between morphological quality of QRS complexes and precise temporal placement of the R peak. Finally, we highlight future directions that may resolve existing problems and allow for reliable and robust cross-modal physiological monitoring using just PPG.