Automated crop classification and mapping is currently a topic of significant research interest worldwide due to the following two factors. First, it is one of the key tasks on which the success of digital agriculture hinges, and second, there is wider availability of remote-sensed imagery, both optical and radar-based, that can help with remote monitoring of crops. Several different models have been developed for the purpose, but a hitherto unexplored geography or time period generally requires fresh ground data specific to the space and time, and, in many cases, fresh feature engineering as well, due to lack of intra-class compactness and inter-class separability. A near-universal model that can be applied with minimal fine-tuning using free and open access satellite imagery and requiring no new ground data, which can reduce data costs, is elusive. This paper underscores the challenges involved via a case study with two different classification approaches at various regions. Methods and techniques that can ameliorate the problems are discussed.