This "wire-with-gain" stuff is a road which leads down to nowhere.
I've heard the KGSS, KGSSHV, BHSE, T2DIY. Despite having a house sound, they do all sound different. The better sounding amps of the bunch, the BHSE and particularly the T2DIY, have a tiny hint of tube sound. That's an error of commission. But they are better than the others because they commit less errors of omission. These amps also have a slightly different tonal balance, with the BHSE being the brightest of the lot, depending on tube.
There is something to be said with the famed BHSE and the SR007 combination. It's a great synergistic combination. The SR007 is a notably laid back sounding headphone (which measurements confirm), but does that imply the BHSE does not exhibit sufficient "wire-with-gain" properties and we should not buy it? Buck no!
Measurements will prove nothing about wire-with-gain. The Objective2 amp despite its excellent measurements is a slightly veiled sounding amp with a strident treble quality. I've done so many different measurements with different amps that I know that two amps which sound different will still measure the same in frequency response, and sometimes amps which measure worse in the distortion department will sound more clear, detailed, and dynamic. (Everyone seems to cite Nelson Pass, well duh.) Heck, just look at decent DACs: almost nothing about their sound can be discerned from looking at their measurements. They all measure very well, very close to each other, yet they can sound very different.
The point being that there is no absolute reference for what is correct or what is not. And I can promise you measurements will show a flat 20-20kHz. But yeah, as an aside, I do subjectively feel that the KGSSHV is very neutral sounding which has a tonal balance which works well for both the SR007 and SR009. Compared to the better amps, it does commit errors of omission though. Oh wait, I guess that means it isn't "wire-with-gain" anymore.
Sorry, but one cannot pick and choose and decide that amps from one designer is "wire-with-gain" in an absolute sense and those of others are not. It's way too simplistic of an approach; and it just doesn't work that way.