I failed to see a declaration by IITs that "JEE is a race to CSE." I don't know when this declaration was made. At least, I didn't get the memo as my first choice during JEE counseling was EE at IITD. Another of my classmates, JEE rank 4 also chose EE at IITD. Yet another of my classmates, JEE rank 16 also chose EE at IITD. This trend is still continuing (JEE 2014):
The opening JEE rank (47) for IITM was for EE not CSE. If you look at the above chart, you will see each of the opening ranks for these branches is higher than the closing rank(51) for CSE, IITB.
By design, engineers should have breadth of knowledge in engineering, therefore they are taught introductory subjects from other branches as well. There would be no point of having computer engineers if those problems were not applicable to other fields. There would be no need of "computational" fluid dynamics (CFD) if there were no fluid dynamics. CS or any other engineering branch for that matter is closely linked to other engineering branches. If you don't know what is going on in other branches, it is really hard to take your field forward.
Moreover, then I would complain, what is the point of testing chemistry, as there is no "need" of chemistry for electrical engineers. Chemical engineers would say that there is no need of "physics" for them and so on. So, how many JEEs would you conduct.
And, even assuming that "JEE is a race to CSE," the village or small town people would almost never get selected if the test were conducted for coding because most such places don't have computer facility or good enough teachers. You would practically have all metro people occupying these seats.
I feel that JEE is good as it is except that I would have a subjective exam as well.