Here is my basic questions. Does it make sense from a theoretical point of view to use the Maximum Likelihood classifier in a multi-temporal dataset of satellite images (Sentinel-2)? I mean, perform a single MLC classification for the complete multitemporal dataset, not MLC for each image.
Yes. It does make sense and it is a very classical way of going about using phenology to classify different types of vegetation.
Using multiple timesteps in classification generally helps separate deciduous from coniferous forests, and farmland from meadows / fallow areas, but it also adds some noise depending on exactly when the two images were taken. These noise elements can be differences in time of plowing of fields, or browning of leaves in different parts of the study area. Another potentially source of noise is actual changes in land cover between the two images were acquired.
All in all, using two or more images for classification is commonplace, and which exact method for classification that you use have limited impact on this (with a few exceptions).