Is there any research work on the usefulness of the concept of "personality" for an AGI? Humans have been endowed with personalities by nature, and it is not clear (to me at least) if this is a feature or a bug. This has been explored in science fiction by various notions of Borg-like entities. It is my belief that, for narrative reasons, such stories usually end with the humans with their flawed personalities winning in the end.
Are there experts who have analyzed, perhaps mathematically, design criteria for an AI agent with weakly enforced goals (e.g. to maximize reproduction in the human case) in an uncertain environment, and ended up with the answer that a notion of personality is useful?
If there are AI researchers, philosophers (or maybe even science fiction) writers who have examined this question in their work, I would be happy to know about those too.
'Personality' is something of a 'suitcase word' (Minsky) for quite a large collection of (presumably reasonably consistent) observable traits. 

It seems clear that there is a certain collective advantage in having a consistent personality - specifically that it affords observers some learning gradient in an otherwise uncertain environment. This is of particular importance because those consistencies might have been arrived at using different learning mechanisms than the ones a given observer has.

Hence, in any non-trivial coevolutionary system, other organisms will inevitably make use of any such consistencies. Consider a simple robot, called Alice, say, that has the trait of 'quickly flashing red when it sees a blue robot'. It makes sense for all observers to exploit everything that they perceive as correlating with Alice's behavior, in particular, the prediction that a blue robot is likely to be present.

The best reference I can recommend on this (which shows that we tend to ascribe 'personality' to even very simple mechanisms) is 'Vehicles' by Valentino Braitenberg.