The challenge of imaging low-density objects in an electron microscope without causing beam damage is significant in modern transmission electron microscopy. This is especially true for life science imaging, where the sample, rather than the instrument, still determines the resolution limit. Here, we explore whether we have to accept this or can progress further in this area. To do this, we use numerical simulations to see how much information we can obtain from a weak phase object at different electron doses. Starting from a model with four phase values, we compare Zernike phase contrast with measuring diffracted intensity under multiple random phase illuminations to solve the inverse problem. Our simulations have shown that diffraction-based methods perform better than the Zernike method, as we have found and addressed a normalization issue that, in some other studies, led to an overly optimistic representation of the Zernike setup. We further validated this using more realistic 2D objects and found that random phase illuminated diffraction can be up to five times more efficient than an ideal Zernike implementation. These findings suggest that diffraction-based methods could be a promising approach for imaging beam-sensitive materials and that current low-dose imaging methods are not yet at the quantum limit.