The problem is that fundamentally, there is a fixed amount of information that there is, that has to be distributed over two dimensions. Particles that are constrained to a small area (e.g. photons going through a slit, electrons bound to an atom) simply do not have a well-defined momentum. In fact the effect is something that you can experience with a sharp enough camera lens: as you close the aperture (therefore forcing the light going through it to be in a specific place) you slowly lose resolving power as the light stops behaving nicely and diffracts around/through the aperture.