The reason is not difficult to find. A good placement after IIT degree may get you a phenomenon salary. It however does not have any public acknowledgement of your performance or position in your company. But IAS brings you recognition at a very young age when you are just 5 to 6 years into the service. IAS offers variety of job descriptions at decision making level which no private organization can offer. IAS also enables you to decide for your country and participate in nation building. By the way the salary in Civil Services is fairly decent by any standard and there is job security.
Approximately 80 to 85 percent seats of CSE are won by the Engineering graduates , mostly from IITs. AIIMS, medical colleges and Law schools contribute another 5 percent.