• The true maximum score isn't known, so all I can ever say is that I've done better than I did last time. I'll never know if I've done as well as I can. By contrast, once I've skipped zero pieces, it's instantly clear that I'll never be able to skip any fewer. So one aspect of a qualitative goal is that you know whether you've achieved it or not. And what makes "score more than last time" a quantitative goal masquerading as a qualitative one is that as soon as you achieve it it gets replaced by an almost identical goal with a different number in it.
• The difference between "non-zero" and "zero" is a much more conceptually fundamental difference than the difference between "lots" and "slightly more lots". If some skips were inevitable and I was just trying to get as few as possible, I think I'd see that as a quantitative goal, but getting none at all is somehow a more "natural" thing to want to know if you can do.
• When I press the skip button, I'm pressing a button that says "I made an error", and I don't like having to admit that, so I'm motivated to try to avoid it. But when I just don't happen to score very many large blocks during the game, it's hard to point at a specific bit where I could have done better. Probably there was some point where a different arrangement of pieces would have scored more, but it didn't jump out at me at the time and make me think "oops", so it's less of an immediate blow to my pride and less of a motivation to go round again and try to do better.

Yes. One of these days I want to invent a new scoring system for Tetris, because I'm sick and tired of the emphasis on clearing large blocks of lines at a time which virtually all existing scoring systems reward.

drswirly is particularly good at playing for tetrises (clearing four lines at a time using an I-piece): I've seen him play Tetris Worlds from level one and end up on level fourteen having scored about thirty-seven consecutive tetrises and cleared no line that wasn't part of a tetris, in spite of steadily increasing game speed. This is of course fearfully impressive (and I suspect even he couldn't have done it without the various planning-ahead features that TW supplies), but although I can admire the skill involved I don't feel motivated to try to emulate it, because the thing I really like about Tetris is something else entirely.

The playing style I describe above doesn't depend on lines actually disappearing when you fill them; it would work exactly the same way if all the pieces you dropped stayed there for ever and the well just stretched at the bottom so you still had some room to manoeuvre at the top. He's just packing a box with tetrominoes, and the line-clearing business is simply a means of stretching the box as he goes along. But what I find really elegant in Tetris is play which depends on the line-clearing semantics in a much more fundamental way, and which simply wouldn't work if you were just packing a box. For example:

Here, dropping the Z-piece at the position shown leaves an unfilled hole below it, but it's OK because the clearing of a line immediately uncovers that hole again, so in Tetris this is not an error move whereas it would be in pure box-packing. Even better would be if the I-piece on the right wasn't already there but was known to be the next piece to drop: you could put the Z where I've shown it and then drop the I down the right, deliberately introducing a hole but knowing you were certain to be able to remove it again immediately. This sort of thing is elegant and cunning and strikes me as "thinking outside the box" in a way which pure box-packing strategies aren't; it's this type of play which makes me feel I'm playing well, and it irks me that conventional scoring systems don't reward it at all (the line about to be cleared in the above picture is a single line and hence the lowest-scoring kind of thing).

Of course, it is hard to invent a scoring system which only rewards deliberate making-and-clearing of holes; all Tetris players are familiar with the experience of creating accidental holes during play and then having to fight their way back down towards them to clear up the mess. If I just rewarded the clearing of a hole, I'd be rewarding doofus play as well as my elegant style of play. Perhaps the emphasis ought to be on clearing holes promptly? So that the example I show above involves a hole being cleared in the same instant as it's created, or one piece later, so it would score lots; whereas if you left a hole at the bottom of the playing area by mistake and eventually fought your way back down to it 200 pieces later, its potential-score-value would have gradually decayed to the point where you barely noticed the bonus for uncovering the hole.