I disagree on a number of points: 1) Depth is not any more synthetic than any other dimension but it is the more difficult one to reproduce correctly because it is so dependent on the accurate retrieval of a lot of low level information that can be easily masked by speaker issues, such as diffraction, breakup and other resonances, electronics issues, such as high order and IM distortions as well as noise and distortion disguised as noise (creating a false, signal correlated floor), signal cables (picking up RFI) and power (much more important than I was willing to admit for a long time).
2) Most rooms will support far more than most people believe they can...once you start addressing the points above you might question the need for much room treatment.
3) More depth and a more immersive 3d soundstage is nearly always in the right direction regardless of the recording...where it might be false is if all recordings sound the same in this manner. There should be a high variability but hopefully you have enough really good recordings to evaluate the changes you would get from recording to recording. Whether a depth is real from the recording or fake from adding of reverb should still be audible as depth.
It is no wonder that once people start addressing these sources of information damaging noise and distortion in their systems that the report blacker backgrounds, more natural highs and timbres and...here it is...improved soundstage depth and ambience as well as more 3d instruments and more accurate placement WITHIN that soundfield.
No one is debating that recordings have highly variable soundstage depth and the best ones go a long way towards giving a realistic portrayal.
Well, those are postulates. I characterize depth in stereo as synthetic because it is the dimension that sounds by far least anchored in the way unamplified music in soundspaces sounds. In fact, it's generally not realistic at all. But it's interesting and engaging to the point where people chase more of it at the expense of more fundamental and realistic imaging. Now, having vast experience over a huge variety of speakers exhibiting various combinations of the distortions you cite -- or the absence of them -- listening to any has led me to the same conclusion. Depth portrayed via any speaker design or type presents depth synthetically, but even speakers flawed in the ways you cite can portray
reasonably natural depth from a certain generation of recordings spanning perhaps less than 15 years. You could get depth sort of grounded in some kind of reality from those recordings even back in the days of zipcord speaker wire, speakers topping out at 14kHz, time-aligned nothing and horrid 1st generation transistor amps circa 1964.
I do agree cleaning up your system is the right place to start. Don't use room treatments to fix systems errors and ailments. Room treatments, if any, should be light. What this industry calls "blacker backgrounds" certainly leads to more revelation. WRT perception of depth, I find that to mostly reveal even more clearly how synthetic it is in stereo compared to width and height dimensioning. Timbre, event clarity, timing are better benefits. Spatially, you almost never know what the real soundstage was and if the recording never had everyone in the same room together, it's totally faked.
More depth than is possible in the real performance isn't the right direction -- it becomes a distortion itself, ear candy as much as high 2nd-order harmonic distortion in old sweet-sounding tube (valve) amps. Reverb, btw, does simulate an enlarged space but it doesn't add to perception of depth in performer or instruments placements in a soundstage. If the recording has reverb added, that's essentially and instrument itself -- part of the plan. But reverb doesn't tell me Brian and Dennis Wilson are relative to each other in the depth dimension. Nor does adding it to make a live recording hall wet, change the placement of instruments and people in an orchestra. Point is, recordings that actually capture reality-grounded depth almost never need placement acrobatics to uncork the depth dimension in the soundstage. You don't have to have your speakers 3-6 feet into the room to hear and have it. When you have to pull your speakers into the room to find depth, that tells me it is not likely there to begin with. It's telling that I usually see people striving for depth optimization using modern multi-track recordings, almost none of which have any actual, natural dimensioning.
Phil