I think user-defineable AR should be allowed, without penalty. I'm a regular player of Flash Flash Revolution and a casual player of stepmania, and the speedmod (which is analogous to AR on osu) can be set by the user to any amount without penalty. And nobody even considers or discriminates against other people's speedmods, it doesn't make any player "better" or "worse", everyone just uses what they are comfortable with. I've seen pro players with speedmods of 1.7x speedmod and noob players with a 2.3x speedmod and vice versa, it's just a matter of personal preference.
If changing AR should change the scoring, then perhaps we should give mappers the ability to also tell us which keys to use, which input devices to use, and which skins to use as well.
I don't see how some people are saying that AR isn't analogous to other speed/scroll settings in other games. One would keep raising it to the point until you can actually differentiate the notes and have a firm grasp of what's going on in terms of pattern recognition (having it too low will just make it look like a blob of notes all on the screen at once with a million approach circles at the same time). You stop raising it when you notice you aren't getting enough time to react and/or you lose that sense of pattern recognition again. Basically higher scroll rates and AR give you more spacing in between notes (easier readability) and lower scroll rates and AR give you more reaction time. It's up to the person themselves to find the middle ground that works for them and this middle ground is going to be different for each person.
I kinda glanced through some of the previous pages of the thread and noticed someone saying how Airman is impossible on AR9. As for me, I can almost pass it on AR9 (I still fail in the ending jumps) but I can't even get past the first minute of it with AR10. Although AR8 on Airman is too clustered and unreadable for me to do well at all. Allowing changing AR would let everyone play it at the speed at which they feel comfortable.
As for complications with other mods. I'm sure flashlight and hidden might have to be tweaked a bit but I don't see much concern there. For doubletime, the reason why the approach rate increases for doubletime is to accommodate for the change of the speed of the map since higher bpm maps are typically a bit easier on a slightly faster AR (like I wouldn't dare play an [easy] map with AR9). The logic is that if a map is at x AR, then it would be optimal for most players to have the AR at ax+b to accommodate for the increase in bpm from doubletime (I don't know the a and b values, or even if it's a linear function or w/e so sorry >.<) This only works though if the original AR is optimal for each particular player which it isn't. Basically what I'm trying to say, is that if you can change the AR of the map with no mods, you should be able to do the same for the DT mod. Also, the mod is called is called "double time", not "double time plus additinoal AR." The extra AR that's added, is there to accommodate for the faster chart, but with user-defineable AR, people can figure that out for themselves.
As for hardrock, I'd just say make it simple by making a 0+ change to AR when hardrock is selected. Hardrock is supposed to make the song harder, in an objective as possible sense, and since increasing AR is an aid to some people, it defeats the purpose of this mod.