You should find some database info through the Human Proteome Project, which has facilitated a number of comprehensive studies.
http://www.thehpp.org/resources.php
At one point, there was a compilation of detected human proteins published through the Human Proteome Organization (HuPO). www.hupo.org Among the projects was a comparison of detected proteins across a number of different labs. Since 2D gels were a common technique, pI should be a primary aspect of the data.
So, the neutral charge, in the circumstance of a relatively pure protein in a buffer with pH matchign pI, often does result in precipitation (and is a dangerous practice for manipulations in the lab, which most of us know to avoid). But in a biological milieu (cytosol, blood plasma, etc) there is a huge amount of other 'stuff' that helps keep proteins in solution. What is the concentration of total protein in the cytosol or in plasma? It's HUGE. Aggregation, which may be an intrinsic early step in some precipitation mechanisms, is not facilitated when there are so many other proteins also dissolved in that same volume. And you also have lots of ions, zwitterions, and other small molecules that all can interact with proteins.
Carrier proteins like albumin also help keep other molecules 'dissolved' when they don't want to be -- an acknowledged biochemical function. But it's also likely (perhaps just my opinion) that the mass of dissolved proteins (per my comment above) act, in bulk, as carriers for the few things that might not want to stay in solution.