Just curious what is the advantage in doing the rips, which presumably aren't as good quality as the discs on a decent BR player.
Don't presume...a MakeMKV rip of a blu-ray is identical video-wise, it puts the video in a different container without any loss. Assuming you have a device powerful enough to play it back, you won't be able to tell the difference. It's your choice whether MakeMKV retains the HD audio as well--I do not--I'm perfectly happy with the extracted DD and DTS core audio because 1) those are quite good and 2) there's no OS X software capable of passing those HD audio tracks as-is through to an AVR anyway. With MakeMKV you lose the menu structure of a commercial disc, obviously, but that has its advantages as well--when you want to start watching a title and select it in XBMC it starts immediately. That's a big reason why we've been ripping dvds for the past decade--to have more control over what we watch and how we watch it.
Mainly convenience and having all your movies browsable on an ATV3 without having to dig through the shelves for a particular disc?
Convenience is the biggest advantage...plus control...to have all of your TV and movies accessible from anywhere in the house...on any device...just like all of your CDs within iTunes. It's the "accessible on any device" thing that really requires moving beyond optical discs--when you're in bed and want to watch something from your collection on your iPad what good is an optical disc? Rip it to a hard drive, then a Mac can serve it up to any device in your house on demand. If that Mac is connected to an HDTV then there's no need to transcode that MakeMKV rip any further.
Do you also view them through a BR player or you just rip and only play back the rips?
I didn't play my first blu-ray disc until MakeMKV released its first beta for OS X, when it did I picked up a 5.25" LG drive from Newegg, slapped it in a USB enclosure, and off I went. So yes, I just rip and play back the rips, but sometimes I transcode those rips with Handbrake as well to various aTV and iPad presets.
So can you access the BR rips stored on those USB drives connected to Airport Extreme from stock AppleTV 3s?
Using an aTV isn't quite so straightforward.
A stock aTV3? No, the only thing a stock aTV2 or 3 can access is what's in your iTunes library, through what's called iTunes Home Sharing, that rules out a full-size blu-ray .mkv since iTunes does not support .mkv, but if you were to convert that .mkv to something that can be imported into iTunes, and if its bitrate weren't too high, then yes, an aTV can play files stored on an AirDisk drive...iTunes doesn't care where you store your media, i.e. where it resides, if you want your iTunes media on an AirDisk drive, so be it.
ATV can "see" the contents of those drives and play the rips directly or you have to use MakeMKV to decrypt/rip the BR and then convert with Handbrake?
The only thing an un-hacked aTV2 or 3 "sees" is iTunes home sharing, it'll see whatever video you have added to iTunes when you have iTunes open on a Mac somewhere in the house--if you have several Macs with different iTunes libraries in the house it will see all of them as long as they are all keyed to the same home sharing ID.
This restriction, if you will, is the main reason why many want to hack their aTVs, to remove the iTunes restriction and turn it into a cheap little box running XBMC that can play anything and "see" external and network drives directly. I have Macs at our main two HDTVs and an aTV1 running Crystalbuntu in a second bedroom which can play back full-size MakeMKV blu-ray rips, so I personally don't really care too much about hacking aTV2s and 3s, I have no need to. I have always had a stock aTV2 or 3 in the living room just for Netflix and AirPlay, though, and love it.
As far as Handbrake conversions go, and whether you want to hack an aTV2, you'll have to figure out what works best for your situation...I ask Air Video to do live conversions a lot streaming to my iPad, which mitigates my need for time consuming offline Handbrake conversions, and I rarely need to physically move content over to my iPad, as a result, most of my video is not "in" iTunes per se. Doesn't need to be.