It's really down to the implementation of the circuit, some DAP's including the DX220 do output more power and utilise multiple DAC's to for their balanced connection, this is true.
For your LCDi4 and 80's music I think you may be confusing gain vs output power. If the louder mastered stuff is loud enough then the quieter stuff should be too assuming there is a gain setting that can present the same overall input level to the final output headphone drive stage.
There is nothing about a 3.5mm single ended connection that limits its power to for example less than 1 Watt, or affects the output impedance of the headphone output stage, or limits the peak voltage that can be output. All of which are critical to driving a lower sensitivity IEM or headphone.
I've seen other's on Head-Fi stating that for portable use and as an output connection choice for a DAP its simply a marketing gimmick and just lately, after trying many different IEM's and DAP's I'm tending to agree with them.
The DX229 and IT04 would be pairing I would imagine would sound sublime over the 3.5mm SE connection.
Often the simplest well implemented solution also is the best sounding, but this will vary depending on choice of DAP and headphone, with the right combination of the two there is IMHO no need to venture to a balanced connection.
I see what you're getting at. In audio, as in so many things, it comes down to implementation doesn't it? Like yourself, I'm a great admirer of the simplest solution, but I think it is, actually, more complicated.
Speaking of amp8 and amp9, It is not unlike the debate between tube vs. SS. Many people also argue that there is no such thing as a "tube sound." They will say that a tube design can sound perfectly fast and clear and a SS design can sound thick and wooly. It is not the topology; it is the implementation. Yes, simply put, yes, but it is more complex than that, right? You can surely design a clean tube and a dirty SS amp. But tubes lend themselves to a certain sound as does solid state, by design. There's a reason why both exist, beyond marketing. Marketing abuses it, it doesn't create or dissolve the actual differences.
I–think–the same can be said for balanced vs. SE. Of course you can build a SE amp that breaths fire and spits lightning, and there are balanced implementations, that are just as you say, weak and pure marketing. But, they each lend themselves to different things, no? In many ways, the simplest solution to well implemented power for DAPs, I think very well may be a balanced design, like the simplest solution to a romantic sound is from tubes--not the only solution, but the simplest.
Likewise, regarding soundstage, are there shelves stock full of SE amps that have wider stages than poorly implemented balanced designs? Without a doubt. But–if all things are equal–I'd bet that the balanced design will have a better separated and wider soundstage (and I love soundstage).
Your point about gain vs output power is also well taken. Yes, I can "remaster" my files with a higher gain setting or I can find an app that has a well implemented digital "preamp" for makeup gain and it will be fine (sort of). I'm actually thinking of doing that just so I can use amp9, for its tube sound, but the simplest solution is just to stick with the well implemented balanced output power of amp8 (grin).