The point is: The current proof of work scheme makes it possible to parallelize and have pools. A pool could thus become a very strong adversary which is not what we want - right? A non-parallelizable proof of work scheme has the consequence that nobody can become stronger than a, say, 4.5 GHz overclocked single core pentium. This is what we want.
If I can get X power by doing Y. How am I not going to be able to get 2X power by doing Y twice? How could you possibly tell the difference between two people doing Y and one person doing Y twice? Not to mention (again) that the pool is actually just a bunch of people separately doing Y and sharing results.