thinking of room modes as standing waves has caused me a great deal of confusion, while thinking of them as room resonances makes more sense
How does it help to pretend that a "room resonance" is something other than a "standing wave"?
Wait.. don't answer that. I'll agree that as long as the discussion is solely about grasping a rudimentary idea of what changes to a room will help achieve a certain result in modal behavior we don't need physics. In that event, any analogy will suffice [provided it remains valid to real physics]. But let's not let using analogies to physics as a shortcut allow anyone to pretend they have changed the laws of physics... or "discovered" something new. That sort of silliness just breeds misconception and wastes folks time AND money.
It's pointless to argue over how one should look at a physical phenomena if the only goal is to grasp a general rule of cause and effect... it doesn't matter in that context... but it is silly to pretend that looking at something differently changes what it really is.
Room modes result from standing waves... but that don't mean you have to learn to visualize wave behavior to understand how to manipulate room modes. Calling room modes something else besides standing waves [Dragon Farts for example], and picturing the physical elements that give rise to them in some creative way that works for you as you go about trying to control them does nothing to change the real causes or limit your ability to make effective changes [though it may help you get your project completed and move on to other things].
We could forget waves altogether. Maybe we should.. it sounds like that would help you in some way... and I have no objection with that goal.
We could just say the room's resonances are driven by interior dimensions and the reflectiveness of the surfaces [ceiling/floor/walls] and taken together they act like a set of large water jugs spread out on the floor and filled to different levels so that the jugs hum at different notes... and its a good thing if the levels in the jugs vary... so you get a nice even mix of tones... none dominating. Maybe, that is enough for practical purposes of understanding how to address room modes when they cause problems... as long as you don't let the analogy drive you into misconceptions on the real physics behind the problem.
A few points on those humming jugs:
1) The lower toned jugs are the worrisome ones - how high up the band you need to be concerned is a function of modal density. If you have 50 jugs in a given octave, they tend to drown each other out, no particular tone dominates... the more jugs per octave the better. Small rooms have low modal density. The problem is worst low in the band, and the smaller the room the higher on the band the problem will reach. So small rooms are more prone to modal problems, and they are prone to these problems at higher frequencies.
2) Modes arise from a large set of dimensions - not just the distances between parallel surfaces [axial modes] - so there are more than 3 of them [and their harmonics]. Instead there are dozens of modes below critical levels of density for any given room. Choosing to look at only the axials is working in the blind. OTOH the axials are the biggest jugs [the loudest] so problems with this set of jugs can cause the worst problems... but happily axials are the easiest to alter [example if the front to rear wall axial matches the ceiling axial, then a broadband absorptive ceiling and a large diffusion array on the rear wall will go a long way to removing the problem].
3) By shifting just one dimension of the room you alter the level in a large number of jugs - this is trivial if you think about it BEFORE the room is built. Best to do your jug level juggling before you build.
4) Broadband absorption diminishes the loudness of all the tones - and all tones exist in corners - broadband absorption in corners will turn down all of a room's resonances - a good place to start.
The point of the above is to agree that we can talk about room modes without talking about wave behavior... and cite a series of examples... but be careful you don't let the analogy become the topic. The problem for me arises when someone wants to say something incorrect about the physics in the context of an analogy, and then insists the analogy is the proper context for discussion... at some point to get the whole picture, and engage in a real debate of all the elements, you have to drop the analogies and talk about waves.
Does that mean it is necessary to dispense with analogy in order for the average person to wrestle with room modes in their home studio? I don't think so, but if we are going to debate various points on the physics behind the cause and effect of room modes, then I think its time for the analogies to go away. And if you want to participate in that discussion... then you need to grasp that room modes ARE standing waves... anything short of that and you're just talking into your hat.