Why would you exert time and energy conjuring up a false persona and deluding yourself into believing it has autonomy

Autonomy is basically a question of free will. Given that various people have argued that humans don't have free will and therefore no autonomy, tulpa probably have no autonomy as well.

If you however grant that humans do have some kind of autonomy in their actions it's very interesting to see if tulpa also have autonomy for the same definition.

This means you can learn something about the nature of autonomy that's useful.