Way back in about 2000 there were a lot of people who were looking at the amazing processing power that inexpensive DSPs had. I can't remember the name of the processor but Motorola had an 8MHz asmetric 3 core processor based on the Motorola 68000 (2 cores were super scalar RISC processors and one regular Motorola 68000 core) that could unencode MP3s; this sounds like a simple task but you required a 200MHz+ Pentium 2 processor to perform the same task.
I imagine Sony choose the Cell because they wanted to create a bleeding edge DSP like processor under the belief that the processing power gains were universal and easily accessable; the problem is that a DSPs are designed for a very specific task (digital signal processing) and it isn't easy to take advantage of the additional processing power and many algorithms run dramatically slower on DSPs.
Think of it this way ... If you have a modern GPU in your PC the odds are pretty good that its floating point performance is dramatically higher than that of your CPU. In terms of Floating Point Performance per clock cycle your GPU is probably 100 times as powerful as your CPU; this is because your GPU has many parallel processing elements for pixel/vertex shading which enable it to produce the advanced materials you see on objects at high resolutions in realtime. It is theoritically possible that Microsoft could produce MS Office to run on top of your GPU rather than your CPU but it would run slower and become a development nightmare.
