I don't know what crossover distortion is, or what digital clipping is, but have you ever played a Plexi? It has a similar kind of character to what you posted, but it really sounds to me that your post is mostly just poorly recorded.
My only point is this: the POD does not sound like your recording when I use it. I'm sure I could dial up something equally terrible if I tried, but I'm trying to make music. So I don't know what your point is. Many people use these things to make really excellent sounding music.
Is it easier to screw the sound up on these--or as others have said, with my old tube amp I could just plug in and go? Sure. More options certainly make anything harder to use. If I wanted easy, that's the route I'd go. But I'm trying to make music.
To me, and I'll grant you it's not everyone's cup of tea, the versatility afforded by these devices far outweigh the minuscule and I'll say "alleged" sacrifice in perfect tonal quality. I'd rather be able to switch between really good models of a Boogie and a JCM800 (in stereo) for a rock song, and go to an AC30 for something quieter, than have to choose one amp and try to make it sound close to all of the above. That to me is a true sacrifice...buying and lugging around a great tube amp for its tone, and then sticking a million pedals in front of it so it can sort of sound like AC/DC once in a while.
Yeah, I hear you, I used to perform in show & tribute bands, I needed a wide variety of tone, hence I've been using Line6 from the original bean, the AX212, variax acoustic, and now the HD500.
I'm also trying to make music; record it, specifically, and I picked up the HD500 on spec because of course the versatility appeals, but I can pick a preset or set up a new tone that is nothing but an amp with a bit of drive, grab my strat, tele, ibanez or gibson, and via XLR, USB or phones, I hear that nasty little clipping sound on top of the tone, and I've spent heaps of time trying to dial it out, hunting forums, back and forth with line6. I assumed for the past two months that my unit was defective, just resolved recently that it's not.
Anyway, I realize it's working for a lot of people, so I was wondering if that's just because they don't notice or don't mind that clippy-distortion sound. Almost all of what I find for recordings produced with the HD seem to be high gain, and of course it's harder to hear that sound in a high gain tone (though I still do) and even harder in a mix. I finally found an extensive thread of people discussing this exact sound, calling it cross-over distortion, and it seems it is a particular issue on the HDs with low gain amps once the drive is up enough to get just a bit of break-up. That's the exact tone some of us want, a nice warm light crunch, hence me only providing the short clip with one tone in spite of it being an issue I hear on almost all presets and amp models.
Anyway, just to be clear, it's not a recording issue. The signal out wasn't too hot, and that sound is there regardless.