Symmetry is ideal in the sense that it needs the least work if ever. That said asymmetrical rooms are used for critical listening environments all the time. The key is to properly define a reflection free zone within that space and build around it to make it precisely that. Like I said, it is more difficult but it is not impossible. There is a large body of math at the architect and acousticians disposal to achieve such a goal.
Over the years I have overseen the design and construction of a number of listening rooms; including six that had build-outs of over 100,000. These had ceiling and wall curvatures to break up modes and focus acoustical energies. I have also done acoustical corrections in a number of environments. I own Solution Acoustics ; which does room treatment systems - inactive presently; due to health issues. Many of the conclusions I've drawn are counter-intuitive to standard reasoning.
There are a number of factors that come into play when it comes to the design of an environment that includes the addition of music; as contrasted to an environment where the principal purpose is the complete immersion into the original event. So there are many more hurdles working in an existing space, as opposed to constructing one from design up.
Most people do not have the space or financial justification for a dedicated listening environment; and so work to achieve the best acoustics within the other needs of the space. In this case, it needs to be decided whether one wishes coverage in a specific zone with the closest recreation to the original event , or uniform coverage based primarily on information content.
If the purpose of a room is specifically for recreating an acoustical event; then the room itself must be neutral to any signature, and be able to allow for expansion of acoustical wave-fronts without any form of compression or non-linearities in energy projection. If the dedicated room is of correct proportions and sufficient size; I would always opt for symmetry, though not always parallelism. You cannot recreate symmetrical development and propagation of energy fields between channels ;; without mirror-imaged paths; referenced to a center line bisecting the room front to back.
I would always set up a system based on accurate retrieval of ambient fields. Anything else can be corrected
I did an 11 part blog in 2014 on room acoustics, but a house fire later that year shifted my priorities somewhat.
Huge spaces with angled surfaces are always the most dynamically open. Perfect symmetry is a requirement for correct spatial propagation of energy. Low ceilings are challenging to work with. Three unrelated commonalities ..
I read an interesting article in Stereophile that was based on work done by Gordon Holt that the ideal room would have the fundamental resonances of the three dimensions of the room ie height width and length 1/3 of an octave apart which would give the clearest sound field
He had gone on to calculate this means the smallest dimension( usually height ) be in a ratio of 1:1.25 the second smallest dimension ( width) and that the smallest to largest dimension should be in ratio of 1:1.6
So for 8 foot ceiling u would get dimensions of 10 ft and 12.8 foot
Interesting my secondary listening room which has always had great sound has by chance almost these very dimensions
It should be noted that there will be no bass below 43 hz in a room that size which is half the dimensional wavelength
Clearly these dimension can be scaled up eg 16 x20 x 25.6 etc
Asymmetry means there will be more fundamental dimensional frequencies which means the ability to keep these apart and not reinforcing is diminished