Why Fizeau interferometers are much more popular than point diffraction interferometers for optical metrology? If somebody wants to measure surface error of for example concave spherical surface - in most of the optical companies around the world Fizeau interferometer will be used, with relatively large, high-precision (and expensive) reference optics (transmission sphere, which will include reference surface).
Why very few are using point diffraction interferometers, where reference wavefront is generated by a pinhole, and is divergent? No large reference surfaces are needed in this case. What are the major disadvantages (I assume there should be, otherwise giants like Zygo would have been doing that)?
 A: As all things in metrology: Because it works better.
It is quite hard to make an ideal hole that is ideally round, ideally small (aka zero diameter) and with an edge that is ideally smooth and consistently formed along the optical axis. And it is not easy to check the hole for these properties.
With a Fizeau interferometer it is possible to check multiple mirror surfaces against each other. This allows to do quality control on the accuracy of the flatness/curvature of the mirrors with the instrument itself, without the need of an additional setup. And it even allows to tell you where on the mirror and in which direction the deviation is. Thus it makes it possible to correct for this error. That said, most people usually start with a reference flat (quite often a mercury mirror) and then calculates the correct curvature from the interference pattern.
Though, recent advances in femtosecond frequency combs will probably make these obsolete. NIST recently demonstrated a system that allows measurements of 10nm uncertainty at a few m of distance using two frequency combs with slightly offset repetition rates.
