There is also the question of whether correlation actually matters for a particular simulation. For example, you have a data structure that must be initialized to some random state. The second usage requires a large number of independent, random sequences. Notice that this problem doesn't depend on the number of PEs, rather the number of bodies. There are theoretical results on other ways to do this, but here is a somewhat realistic scenario that I could imagine implementing.
File access is fast and easy when the file is binary.
In general, the seeds themselves may be a set of values that represent state. Notice that this method is not truly scalable. The file we use needs to be generated off-line, which means either the sequence needs to be enumerated or the generator must have a way to move ahead more than one element in the sequence. Moreover, as longer simulations are performed, longer sequences are required, which adds to the problem. Of course people continue to work on random number generators and computers are getting faster, so perhaps such a method will scale.