Push-up greens are made of native soil, with some amendments added. So the term "push-up green" literally means:
"inconsistent from site to site green"
You will not encounter consistent native soils from course to course. So every push-up green is going to have different drainage and fertility characteristics.
The USGA has always been dedicated to providing guidelines for uniformity. And it has done an admirable job of providing those guidelines. Is the USGA green perfect? No. In fact it comes with it's own set of problems. But when they are built according to specifications, they can provide great playing conditions for many years.
Additionally, the USGA Green is a very quick grow-in. It is ready for play by June, if it is seeded before September of the previous year. I'm not so sure that that could be accomplished with a push-up green.
The USGA green requires less surface drainage than a push-up green. And at today's speeds that is a significant consideration. For if you built a push-up green at the grades that are required to provide fair pin placements, with today's speeds, the surface drainage of the push-up green would probably not be sufficient to grow healthy turf all around every section of every green on the course. Some areas of some greens might struggle. I myself would be concerned that the push-up green would not be healthy unless I had steeper slopes and grades to shed the water, and in that management schema, the speeds would have to be kept slower.
With the older, original push-up greens, you generally have enough surface drainage to balance health issues, and the loss of fair pin placements were acceptable as the speeds evolved. That may sound contradictory - maybe because it is.
In either case, most all of the older push-up greens now have a nice layer of sand topdressing built up so that they are draining as good as newer USGA greens do.
Actually, an older push-up green, with sand topdressing buildup, is the best of both worlds. You get the drainage and firmness of a USGA green, with the fertility storage and soil chemistry buffering action of the native soil.
If you could build a push-up green, and start sand topdressing it after it is grown in, and not push it to speed too quickly (maybe over a three year period) that would be the best way to go.
Another good way to go is to harvest the layers of sand topdressing and native soil from old push up greens, and then reuse them in the construction of a new green. That has actually been done quite successfully at a few clubs.