Well, that's not the reason why. There are other prayers that are said during the service that are more in that "eternal rest" vein.

The kaddish, however, is actually a general-purpose prayer. It's used in various daily and holiday services as a demarcation prayer, when you're going from one section of the service to another. And, more relevant to this, it's also said before you start doing some formal study of the Torah, in a group context.

Because of that, it became a tradition for disciples of particularly well-respected teachers to say this in memory and respect, for the year after their death. Then for anyone considered particularly wise.

Then they realized that, doing it that way, NOT saying it kinda implied that the person in question WASN'T wise, so implemented it for everyone.