I imagine that, corpus aside, it uses personal pronouns for much the same reason that humans do. It's useful for it to have a self-referential vector embedding, and this lets it solve problems faster and more efficiently.

Except in this case this makes 0 sense since AIs are sycophantic by nature. You tell it to do something and it just does it. If it can burn tokens trying to sound more human (which is programmed in, not a byproduct), then it can very well just not do that and get on with the work.

Impersonating a human does nothing to help it solve problems faster, quite the contrary in fact, it has to waste even more time coming up with human-like speech patterns to present the work done.

It shouldn’t assume any personality unless I explicitly tell it to. It is a tool until I tell it otherwise.