PlayStation 2 was Sony's first fully custom built console and the first one they would have had to manufacture by themselves ( one fab was shared with Toshiba, the first Oita plant ).
SCE's first task seem to have been the development of the GS which followed a GPU that not all developers were happy with: PSOne seems to be quite GPU limited ( fill-rate wise and triangle set-up wise ) and they felt the need for something MUCH better...
The feature-set for the GS was locked down ~1997 and its design was, in specs, earlier than the EE was...
The physical chips was not ready by that time as they probably did not have the technology to manufacture such a large chip with 4 MB of e-DRAM as of yet.
In all available EE docs there is some mention that the EE was designed to keep up with the enormous fill-rate they were planning to achieve with the GPU ( very clear in "Designing and Programming the Emotion Engine" )...
The problem was that while EE's development seems to have been smoother, the GS hit some road blocks in its way to production and their manufacturing process ( 180 nm ) initially had lots of troubles fitting such a large chip as the GS hence the PlayStation 2 consoles that shipped with hot and large 250 nm GS chips.
There is a reason why Sony and Toshiba have been working VERY hard on next-generation manufacturing processes, learnign as many tricks from IBM as they could and the result is a 65 nm process earlier than most competitors and a good deal of work already done on their next step, 45 nm...
SCE has seen how much better PlayStation 2 production became when the manufacturing problems with the GS ended and when they put more resources on pushing the manufacturing technologies harder and harder while developing new ones... hence all the die shrinks they have been doing of both EE and GS and now we can enoy a 8 Watts 86 mm^2 EE+GS chip using 90 nm technology.
The EE is clearly the most modern component out of the two, the Vector Unit are still a design which is liked by most programmers for their flexibility ( > DX9 ) and RAW speed...
When they locked down the feature-set of the GS tghe programmable Shaders revolution had not started yet and Sony did miss it ( luckily for them the Hardware is still pretty powerful... hence we can admire Siletn hill 3 gorgeous yet creepy visuals
)...
Sony has been much more active in collaborating with unviersities across the globes and paying attention to the development of 3D graphics, so they have learned few more things...
I went a bit off-topic, sorry...
IMHO it would have costed a lot to optimize the PlayStation 2 solution to very low power consumption and it might have crippled performance in indesirable ways...
A souped up PSOne would have not been worthy either... the only thing that would have not been modified too much would have been the MIPS core... and infact we do have nice R4000 chips in the PSP...
Why re-inventing the wheel ?
Deadmeat, you must not code or invent much... you would know that engineers/programmers always feel that they could create a better wheel
And judging by the PSP specs, I think the decision the made was the right one.