Finishing PhD early and becoming my PI's postdoc instead I'm PhD student beginning my third year. I plan to graduate at the end of my fourth year, leaving me with about another two years in the program. However, at the end of a productive summer of research, my PhD supervisor has mentioned that I'd be on track to finish considerably earlier if I want to. My program uses the "three papers" dissertation model, so at any given time, it's pretty easy to gauge how close we are. 

In fact, I do not want to finish early because I am really enjoying doing research with my supervisor and feel that I'm receiving outstanding mentorship from him. Additionally, four years is already fairly short for my program (which is usually done in five years), so it doesn't seem that there is much additional benefit to finishing before year 4. 

Instead, I'm considering asking my supervisor if I should defend early and then become his postdoc for whatever remains of my planned four years. I imagine the benefits would be:


Since I plan to apply for faculty positions after this, I would have nominally "done a postdoc" instead of being fresh out my PhD. 
I'd be off the hook in terms of departmental responsibilities, like TAing, for my fourth year. 


Are there other advantages or disadvantages to defending early to become a postdoc? Also, are there advantages or disadvantages for my PhD supervisor?

More notes / responses to questions:


I have reason to believe that postdoc funding would not be an issue, so perhaps let's not focus much on that.
It may be relevant that my PhD supervisor and others believe my publication record (from before my PhD, totaling around 17 papers with ~7 first authorships) to be competitive for a faculty position without doing a standard postdoc (i.e., not the truncated version with my PhD supervisor that I'm proposing).
I had an early start with research and didn't go straight from undergrad to PhD


UPDATE: 2 YEARS LATER

After weighing the various pros and cons pointed out here and in live conversations, I ultimately did follow through with the above plan. It worked out great. I am a few months into a faculty position now. It's too early to say if I'll secure successful grants, etc., but I am having a great time and feel very well-prepared. Of course, YMMV, and there were certainly multiple elements of luck, but my n=1 experience with this unusual plan, at least, has been excellent so far.
Regarding potential downsides for you:

"Time since obtaining the PhD" is often taken as the academic age, so by graduating early, you make yourself appear older. This can have a formal impact, for example, many grants meant for postdocs come with age restrictions, so are only available in the first n years after obtaining your PhD. 

[Side note: This wouldn't matter for you if you get a faculty position straight away, but at least in my area, this would be quite unusual.]

The academic age can also play a role informally if people have to judge your productivity. (Number of papers)/(Years since PhD) is a formula I've seen a few times in this context.