Knowledge of the spatial and temporal characteristics of solar surface irradiance (SSI) is critical in many domains. While meteorological ground stations can provide accurate measurements of SSI locally, they are sparsely distributed worldwide. SSI estimations derived from satellite imagery are thus crucial to gain a finer understanding of the solar resource. Inferring SSI from satellite images is, however, not straightforward, and it has been the focus of many researchers in the past 30 to 40 years. For long, the emphasis has been on models grounded in physical laws with, in some cases, simple statistical parametrizations. Recently, new satellite SSI retrieval methods have been emerging, which directly infer the SSI from the satellite images using machine learning. Although only a few such works have been published, their practical efficiency has already been questioned. The objective of this paper is to better understand the potential and the pitfalls of this new family of methods. To do so, simple multi-layer-perceptron (MLP) models are constructed with different training datasets of satellite-based radiance measurements from Meteosat Second Generation (MSG) with collocated SSI ground measurements from Météo-France. The performance of the models is evaluated on a test dataset independent from the training set in both space and time and compared to that of a state-of-the-art physical retrieval model from the Copernicus Atmosphere Monitoring Service (CAMS). We found that the data-driven model's performance is very dependent on the training set. Provided the training set is sufficiently large and similar enough to the test set, even a simple MLP has a root mean square error (RMSE) that is 19 % lower than CAMS and outperforms the physical retrieval model at 96 % of the test stations. On the other hand, in certain configurations, the data-driven model can dramatically underperform even in stations located close to the training set: when geographical separation was enforced between the training and test set, the MLP-based model exhibited an RMSE that was 50 % to 100 % higher than that of CAMS in several locations.