There are no Par 2's, nor should there be IMO, and the rest of the PDGA. They tried this in 2001, and abolished it in 2002.
The minimum par is 3, as it should be. Even though I agree with many points, the simple fact is that you have to allow a shot (drive), an attempt to get to the "green" (see my earlier comment) and then a chance to make it. I personally feel as though the "green" should be about 2-2.5x what it currently is, somewhere between 60-75' should be considered the green.
And Par for competition is required, though it is not as important because ultimately score matters, but in the absence of a player, our rules are set in place to allow for the standard. That is why you see more inflated pars at larger events. It punishes a player for missing a hole that maybe more difficult to achieve a 3 on in normal play, hence the 4-5's that show up on courses that you would not normally think of. Why cliff drive has a par 4 on long 13, a normal player may go OB and end up with a 6 relatively ok, and then have a player show up late and only gain one stroke, not fair. Having that player take an 8 though is much more fair, and punishable accordingly.
17 at WyCo, I have seen 3's there by a few people, Hemmeline almost got a 2 (Freaking lefty lines on that hole with his arm are sick!) I however am always glad to get a 4, and feel that it is a par 4, one to get past the trees, one to get up closer, then I should be on the fringe of the green and have 2 shots (my green here not 10 meters).
You could also throw out all of this and go strictly on distance, and create a standard that way. There have been many comments and suggestions on par, do seom research not only in here, but also the PDGA forum for more questions to lead to more questions, to lead to more questions, to more dicsussions, to more questions, and well were back where we started (as Ray Daives would say)