I disagree with the idea of using some kind of digital emulator. These programs re-process the music and you distinctly lose clarity, negating the point of using the Hugo 2 in the first place. This loss I find far more disagreeable than the tube amp I have.
«Re-processing» is an ugly word for mere DSP, as it implicates a massive signal deterioration, including the infamous breaking of «bit perfection». But if you categorically dismiss DSP, you're also not allowed to use equalizers or digital volume control. Among those there are enough well-implemented examples to disprove the claim of lost clarity and transparency. In my case the equalizer (Neutron) even enhances clarity and transparency – by removing masking effects by dominating frequency bands, without affecting small signals in any way.
Of course (tube-)amp emulators will degrade transparency to some degree – just like added real-world amplifiers. You seem to ignore that this feature is exactly what those users want: A (in their case analogue) sound processing with the ability to mask the headphones' tonal shortcomings. If you use a well-implemented amp emulator and limit yourself to a modest dose of well-mixed harmonic distortion, you should achieve similar results. Apart from sound effects other than harmonic distortion, such as «cable sound» from the various signal paths.
To be honest, I haven't occupied myself with tube-amp emulators (have you?), and although my suggestion is serious, not polemic, it is meant to demonstrate the absurdity of a useless amplification stage with the function of a one-trick effect device. Note that I'm not disputing the sonic benefit in the respective cases (corresponding to the listener's sonic ideals), it's just that you could do better if you're interested in ultimate lifelikeness and transparency – and saving money. Of course that's not just a dogmatic pretension out of thin air, but derived from extensive experiments during my own audio jouney, which I'm on since 50 years or the like.
The popularity of external amps stems from the expectation of a real technical benefit in the sense of higher accuracy, better control and higher dynamics – derived from the usual case of a DAC with headphone output that is bypassed if you use a «better» amp. And many users like the extra warmth, oomph, roundness and forgivingness they provide, thus seem to be confirmed that the sonic result be «better» even in the case at hand where they offer no objective benefit. I don't dispute their sonic preference at all, just suggest a valuable alternative for adventurous audiophiles striving for ultimate transparency and realism. And I do mean realism (and musicality!), not anemic analyticalness!
You're probably right, I should have said $8,750,000. But the number doesn't matter, it just serves to illustrate the impossibility for a preamp to accomplish the signal integrity of a piece of wire.
FYI, an integrated amplifier is a switch box and a power amp with a volume control. A power amp with a volume control is just an integrated amplifier with one input, or maybe two if you can choose between balanced and single ended. There is nothing special or lucky about it. A pre amp and a power amp are, all else being equal, not going to damage the signal any more than a power amp with a volume control does.
An integrated amplifier usually consists of a preamp and a power amp, integrated in one housing. Some of them have a pre-amp output for the connection of a separate power amp.
There are a few exceptions, where the pre-amp stage is entirely passive (Creek, Ayre, Gryphon...).