A good piece of news, directly from ESA's S2 project manager: ESA is now making plans for a global reprocessing of Sentinel-2 archive in 2019. As explained here, Sentinel-2 data multi-temporal registration isn't perfect yet. It should be improved in the first quarter of 2019, thanks to the use of ground control points obtained via automatic matching, but the issue with the reprocessing of Sentinel-2 archive had not been addressed. It is now, but of course not before 2019.
I let you imagine the amount of processing required to do so for the complete 3.5 years archive of Sentinel-2 at that time, so it will be costly and require hard work, but yet it is indispensable. Let's thank ESA and Copernicus for considering this and letting us know !