OK, breaking this into two parts, first talking about the bass region of the curve, which is the biggest problem with XT32: Very simply a curve allowing for a rise in response in the bass region as some of the higher end room EQ systems do (or can do).
When you place a common speaker that measures flat anechoically into a common room, you will get room gain at lower frequencies giving you an in-room response that rises at lower frequencies. This is normal and "sounds flat" to listeners. It's what you expect to hear. Of course depending upon the room, listening position, where it's placed, etc, it's likely to be uneven without EQ so there is likely plenty of room to improve, but when you EQ all of that gain out of the speaker to give it a flat in-room response, it sounds like you've "sucked the bass out" of the speaker to listeners...because you have.
So I think Audyssey could be improved a bunch (especially for those who don't want to mess with the App) by simply having another (or better yet, several from which to choose) target curve that reflects this. Something on the order of the preferred room curves found by this study:
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In the Olive study mentioned earlier, you can see the room EQ systems that were most preferred all had a substantial rise in response at lower frequencies:
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As you can see next, curves that have a substantial rise at lower frequencies "sound flat" to listeners, curves that actually are flat in-room sound like the bass has been sucked out:
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I believe that's the #1 reason so many users feel the need to crank up the sub level 3-6 db after running Audyssey. That's a poor band-aid, however. This causes a large overlap in the crossover region (expanding the "region") which can cause integration issues, and if you have good speakers there's a pretty good chance that at 100, 120, 150 hz, etc, your speakers sound better than your sub does (individual setup dependent, of course).
So while cranking the sub up a few db might restore the overall balance, it's just "not the same." This, I believe, is why so many who actually use and like Audyssey for movies will still switch to "Pure" mode stereo when listening to music--their big towers sound much better when the bass is restored to them, even if they don't extend quite as low, and their subs which were designed to hit the lowest extension they can from the smallest box possible just don't sound as good playing the mid-bass, upper mid-bass, localizable frequencies.
I believe the best of both worlds (easily obtainable for the average guy, at least) is when the speakers and the subs are both EQ'd to the same curve with this rise, so the bass is restored to the main speakers, the crossover crosses over where you set it and both the subs and speakers contribute to the rise--preventing the subs from drowning out the speakers at much higher frequencies than they should for your particular setup.
Luckily this can be done with XT32 and the App but it would get many users who won't go through the effort a lot closer more easily if Audyssey simply had a couple different target curves to choose from that weren't "flat bass."
The second part--the midrange/high frequencies of the curve, gets a bit more complicated. Two different speakers that both measure flat anechoically on-axis, can give very different in-room responses depending upon their directivity (even assuming both speakers have good, smooth, directivity curves--leaving out speakers with "problems" for now). That's what I meant with the "curve appropriate for the speaker" portion.
That's not Audyssey-specific, but more of a comment of Room EQ systems in general. If you mismatch a speaker's expected room curve you'd derive from anechoic measurements significantly, you can really mess up the sound. This is one reason why many say it's a safer bet to limit the correction to the lower frequencies only. A full JBL Sythesis system has the advantage of detailed anechoic data for the speakers being used by the EQ algorithm. Short of that you need to make educated guesses.
An example that should be easy to follow, is a speaker with relatively narrow controlled directivity over a certain frequency. Even if it's flat anechoically, the in-room response will show a large drop in output in the mid-high frequencies since room reflections are limited. Since we tend to key in on the direct sound, the speakers don't "sound like" they're lacking output in the range and may sound quite flat, but room EQ software will see that big drop in the room response and "flatten it out." That can make the speakers sound forward/bright/lacking bass, etc.
If you start watching this interview of Paul Hales at 44:00 (I'd suggest watching the whole thing if this stuff interests you) he explains this pretty well:
And that's just one example of how EQing full range can cause issues. I was just saying that a test where the target room curve was a huge mis-match to the speaker would make for a poor test of the EQ (provided the curve is adjustable, as it is with XT32/App and higher end correction systems).