I'd disagree, at least among the people I know: they all have cheap HTIB systems and the single biggest, most cost-effective improvement you can make from there is to buy better speakers.
No, even in that case, the room can still overpower the speaker. A $200 HTIB system in a properly treated room will sound a lot better than $28,000 Wilson Watt Puppies in a bathroom for example.
Hum, my experience (I was sound engineer in a previous life) is that the first thing to fix bad sound is to flatten the equalizer and to remove bass enhancer. Then I'd put the speakers on a solid table in a relative symmetry regarding the listener, while checking they have the correct phase. All the rest is rarely necessary.
Sure, but that's a rather contrived example-- most people have a fairly normal room, and the average joe would be best served by getting a good pair of speakers, and a reasonable amplifier and DAC, before worrying seriously about room acoustics.
I'd even skip the dac (I mean I might not.... but a decent amplifier, and I just mean decent, like something that still works from the 70's or 80's) and a decent pair of tower speakers (needn't be expensive), and, well, just don't use the shittiest cables you can find (I mean as long as they are thicker than a few human hairs you're okay)- it'll sound far, far better.
You might be surprised how much of a difference EQ can make. As an experiment I once used 12 bands of parametric EQ to adjust the speakers in a cheap, old LCD monitor. Sure, you're not going to get any better bass response than before, but stereo imaging (nonexistent before EQ, perfect phantom localization after), spectral balance, clarity, distortion (due to not exciting resonances in the monitor), etc. were significantly improved. Most people could have added an EQ'd subwoofer to those tinny LCD speakers and been completely satisfied.
One of the many things EQ can't fix, of course, is room reflections, which can be helped by room treatments and speakers with a directivity better suited to the room.
Of course EQ can help with room reflection! In a square room you'll have a resonance at a given frequency, and you can mitigate a bit this problem with an EQ. But usually EQs are used too add bass and do more harm than good.
By room reflections I mean higher frequency reflections that result in comb filtering and spatial and temporal smearing of the sound, rather than lower frequency resonances that result in the standing waves you mention. EQ can reduce the effect of room resonances, but it still can't fix the extended decay time at those frequencies[0].
[0] DRC can improve this, but only within a small sweet spot.
Then you can worry about your room.