I'll start by commenting on Hugh's original points, this'll be a lengthy post so for anyone who doesn't have the time I've provided Cliff notes at the bottom

1. Definitely - any hi-fi amp should at least have "acceptably" low amounts of THD (as opposed to "vanishingly").
2. Sounds completely logical to me. Same happens with speakers - the off-axis response has less HF.
3. If losing HF is unavoidable, harmonics should be compensated for but I disagree that this should happen at the playback stage. It should be measured and compensated for at the recording stage. All recording devices are unequal and one amp cannot hope to accurately complement the deficiencies of a wide range of music.
4. Tubes do add some nice harmonics, but as above this shouldn't be necessary in theory. In practice, we have a lot more control over the playback stage than the recording stage, hence the dilemma!
5. This should be done with a careful ear towards getting the "sound" that the artist wants. At this point it's a question of impressionism rather than brutally accurate recording.
6. Logically I agree, although I don't think low order should be added to mask high order. The high order should be removed instead.
7. Agree that this makes the sound more likeable, but would consider pushing the level of distortion lower than that if we're in the pursuit of "hi-fi" rather than simply enjoying music.
Having an amplifier that adds 2H/3H information to the signal is not "high fidelity" in its purest sense, unless the amount of distortion added is negligible. At the end of the day you are colouring the sound - Doug Self made a comment that amuses me about an amp having a "niceness" knob adding low order distortion to the music.
That said, no amp produces ZERO distortion. If an amp does have to produce SOME distortion, I'd rather it be "musical" 2H/3H tones rather than high order stuff that sounds nasty.
The obsession with THD figures does not guarantee good sound by any means. I have heard systems in the past which sounded clinically accurate and incredibly boring. All of the components measured very well, and yet the final system lacked "involvement" in the music. This is why I screw my nose up at anything Leo Simpson is involved in. He's a measurabator through and through.
If we're not talking about hi-fi then all arguments become null and void - if someone wants to colour the sound artificially by adding 2H and 3H then they should be allowed to. Just don't pretend that the result is high fidelity. This then leads into the great murky grey area - should we be pursuing ultimate accuracy or ultimate enjoyment? Like Hugh said, there are SE triode amps out there with 2% THD that "sound fantastic".
Personally, my demands for a playback system are that it is "accurate" and "enjoyable" - these are general rather than absolute qualities. I don't subscribe to deliberately colouring the sound, but neither do I have any desire to chase the ultimate measurement. A distortion analyser will not give you a complete picture of an amp's behaviour, neither will just listening to it. Measuring tools and the human ear behave in completely different ways (the ear is very non-linear yet adept at picking out things that are lost on a CRO trace). As such an amplifier designer should use ALL tools that are available to him and use them to their strengths. If an amp measures badly then it indicates a problem. Likewise if it sounds awful.
So that's the hi-fi part out of the way. Next, as I briefly alluded to in point 5, at the recording stage it's often the case that tubes are God. Why? Because they DO colour the sound, and the clipping behaviour is completely different. This is not a pursuit of fidelity, it is an artist using the tools they have to express themselves by creating sound (same with different pickups and mics and all that jazz). Even in my very limited music collection I don't have to go past Lenny Kravitz for someone who uses tube distortion to great effect in his music. Would Lenny be as good if he used a transistor mic without an "overload" setting? Course not! Lenny decided what he wants it to sound like. What if I now say I want another 2% of 2H distortion so his voice sounds warm and fuzzy? That's impressionism on my part. Clipping should "never" enter the picture in the playback phase however. That's an example of gross alteration of the signal and the "soft clipping" ability of tubes is of limited use IMO. The occasional light clip at loud volumes is practically inaudible in solid state land, and fixing it requires only a mild tweak of the volume to make your ears bleed a little less

I came across a great quote a while ago, and can't for the life of me remember the author or the full quote. Essentially it said that in science, you must pursue further knowledge based on what you already know while keeping your mind open to totally rejecting your previous beliefs. We once believed the earth was flat and the centre of the universe. 'nuff said.
In my experience there is NO DOUBT that there must be something in the "high-end Audio land" that verifies your idea that we may actually need to deviate a bit from "accuracy" in order to better re-create the actual event.
I think you're heading down the right path with that comment. But any deviation from accuracy needs to be taken carefully. As a designer you should always be asking yourself WHY you are disregarding a measurement or listening test. For example, Hugh's use of a simple resistive feed for the LTP and a resistive loading
I credit Hugh's focus on empirical data and listening tests backed up by sufficient measurement to indicate that the performance is good. It's a pragmatic way of designing things because at the end of the day, we're using our ears to listen not an electronic meter! The objective, technical specs like THD, slew rates and frequency response are indicators to good performance, not guarantors. They should be treated as such (ie approached with equal parts eagerness and caution). If I was designing an amplifier I would use component spec sheets, measuring tools and listening tests in tandem.
Cliff notes
* Amps should measure "well enough" to be classed as hi-fi, and this should be backed up by empirical tests which indicate the amp is an enjoyable listen.
* Multiple measuring tools should be used, and used to their strengths. The ear is also a measuring tool (very non-linear yet exceptionally adept in many ways).
* Small amounts of 2H and 3H are permissible in preference to higher order distortion. However I don't believe lashings of distortion are necessary to enjoy music.
* Any amp which has high distortion characteristics moves from "reproduction" to "impressionism". If that's your game and you enjoy it then more power to you. It could be an aurally orgasmic experience, just don't call it "hi-fi"

* The distortion and clipping behaviour of tubes can be used to great effect in the production of music, but I don't believe them to be necessary to good
reproduction.