How can bass room modes be considered a character of the system in all locations? What might be a peak on the left side of the couch could be a null on the right, a global EQ in the signal path can not solve both these issues. A global signal adjustment can attempt to solve a bass issue at one location, but not both. Or, it can attempt to address them both and try to minimize the RMS deviation in FR, which is what Audyssey does.
For my example, I have a bass peak on the left of the couch. How does knowledge of this peak help to improve Audyssey's performance at my main LP? Would it not be better for Audyssey to ignore this huge problem at a seating location I don't care about, and instead focus on the FR at the prime LP?
Obviously, in your example of a peak and null at the same frequency at different positions on the same couch, even Audyssey wouldn't try to sort that out. However, that's not an entirely realistic situation either. More often, you'll have somewhat different peaks and nulls in in different positions. If they vary that much in a small change of location, like seat to seat on a couch, they probably aren't extremely low in frequency, like perhaps 80Hz to 300Hz. In that case, taking measurements in different positions might actually help Audyssey make some meaningful adjustments for you. Remember that they system measures every speaker in every mic position, and from that data develops filters for every speaker. So those peaks and nulls may be partially compensated by individual speaker filter adjustments.
Audyssey isn't a miracle band-aid for every situation, and it's not that hard to find one that is beyond it's capability to fix. As an example, a severe null, deeper than 9dB won't be fixed because Audyssey has a maximum gain of any filter of 9dB to keep you out of power amp headroom issues. And if all the measurement positions general horribly erratic data there's not much that could be done to create a valid filter.
Keep in mind, however, that a single Audyssey measurement position
is invalid, because it places complete focus on a microscopic point in space. Compensating for response at that point would simply be micro-managing the situation. You don't listen that way anyway, you have two ears spaced by a few inches, and will probably move your head a few inches as well. Audyssey's precision is in its ability to sort out severe, and unique anomalies, de-emphasize them, and create a filter based on similar anomalies over an area. You define the area by the choice of mic positions, but a single point measurement in an acoustic space is never really meaningful, not for Audyssey, REW, spacial/temporal-averaged RTA measurements, TEF, MLSSA or any other type of acoustic measurement system.