I was actually just on my way here to request an option to sort by approach rate. This will make finding maps to practice at a specific approach rate much easier, especially for those (like me) who aren't familiar enough with the different approach rates to say one map is a 6 while another is a 7, and then practice the 6.
This would be useful to any user who wanted to practice higher ARs, and would not clutter the play screen at all.
However, I don't think that actually showing the AR while in play mode is necessary because it would just add a bit of clutter to the screen. The AR doesn't change throughout a map (as far as i know), so simply displaying it on the song select menu would be enough to serve the purpose of making a map's AR easily available to players.
OP: If you change the topic to simply adding a Sort by AR option, this will get my +1