New 4th-generation synchrotron sources, with their increased brilliance, promise to greatly improve the performances of coherent X-ray microscopy. This perspective is of major interest for crystal microscopy, which aims at revealing the 3D crystalline structure of matter at the nanoscale, an approach strongly limited by the available coherent flux. Our results, based on Bragg ptychography experiments performed at the first 4th-generation synchrotron source, demonstrate the possibility of retrieving a high-quality image of the crystalline sample, with unprecedented quality. Importantly, the larger available coherent flux produces datasets with enough information to overcome experimental limitations, such as strongly deteriorated scanning conditions. We show this achievement would not be possible with 3rd-generation sources, a limit that has inhibited the development of this otherwise powerful microscopy method, so far. Hence, the advent of next-generation synchrotron sources not only makes Bragg ptychography suitable for high throughput studies but also strongly relaxes the associated experimental constraints, making it compatible with a wider range of experimental set-ups at the new synchrotrons.