The traits and restrictions are done through the character trait file. But the spawning and deletion of specific generals, used for client rulers, must be done via script. The script needs to know the "name" of the client ruler in question, and it can only do that if it spawns a general with a pre-specified name.

You could move a family member into a gov4 city and then have the traits/restrictions apply to him, but then he is still a family member acting as a client ruler, which defeats the entire purpose of having a puppet ruler feature in EB. It also gets into interesting questions of what happens when you destroy the gov4 building. Does the FM revert back to being a regular FM, does the city revolt and he gets pushed out?

And, if so, only one per city w/o additional script?
Any generals recruited must use the trait file to apply any traits to itself. So no building recruitment ability can do that for you.

Any potential changes in order to setup a different puppet ruler method of implementation would probably break saved games due to the amount of alteration necessary for the trait file.