Can the elements in a complicated room cancel/balance themselves off so that it ends up being a good room for sound. For example, slanted, high wooden ceilings and wall-to-wall carpeting, and windows and absorbing furniture all seem as though they add weight on either side of bright or muffled, but perhaps they can cancel each other out?
So close to the truth.
Every surface reflects, diffuses, or absorbs, to some degree or other. A book shelf full of books all the same size and lined up is just another wall. The same bookshelf with books of different heights and thicknesses some sticking out others shoved in, is a quadratic diffuser. The worst sound is a bare rectangular room with nothing in it, because the parallel walls bounce all frequencies creating lots of cancellation and reinforcement and uneven response.
In the vast majority of cases what happens is the midrange and treble ranges are handled pretty well just by normal furniture and decor. What few problems remain are pretty easy and obvious reflections that either can or cannot be handled, usually depending on factors having nothing to do with audio. Windows, doors and spouses being high on the list.
The same physics that dictate the above also dictate why almost everyone has the same problems almost without regard to the room. This is because low bass waves are 40, 50 feet and more. At that scale all our rooms are almost the same. This is why almost everyone has the same bass mode problems.
These problems can be solved with a lot of big expensive acoustic treatments. Or they can be solved with a DBA. Your call.
Either way, what we come back to each and every time, what I said in the beginning, there is no one thing more important than any other thing. There’s more than one way to skin this cat. Or beat this horse to death. As the case may be.....or as usual.... is.