An unexpected idea...
First, it should be obvious that thickness needs room to expand, but I didn't really grasp the reason before.
In an exchange of territory for thickness, it is crucial for the thickness (or influence for that matter) to be put to work. The move that expands it or makes it work is going to be really big in value, because otherwise the thickness will end up as overconcentration. In other words, if you take thickness and expand (or attack) from it, then you are being efficient, but if you fail to do so or cannot do so, then you will just end up with a lot of stones close together.
Likewise, if you play an erasing move, it is very painful for the opponent, because it causes them to play either close to their own stones, or where they have little chance of succeeding anyhow (i.e., the very area they sacrificed to get the thickness).
There may be bigger-looking moves, but because of the exchange behind it, the thickness-expanding/erasing move tends to be urgent, because it is the one that justifies or renders unfair the exchange.I arrived at this viewpoint after doing a number of fuseki exercises, in which the answer often seemed puzzling, until explained in this way.

Not the best possible example, but es klappt
- Click Here To Show Diagram Code
[go]$$c Not the best possible example, but es klappt
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . . X . . . |
$$ | . . O X . . . . . . . . . . . . . . . |
$$ | . . X . . . b . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . a . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
In this position, Black and White have exchanged a contract. White has granted Black a certain amount of influence in exchange for the certain territory in the top left.
There are many plausible moves. You could, for instance, treat the top left lightly and make a sanrensei at A. You could play lightly at B. You could play out the ordinary joseki, and get this position:

Not the best possible example, but es klappt
- Click Here To Show Diagram Code
[go]$$c Not the best possible example, but es klappt
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . 2 . . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . . X . . . |
$$ | . . O X . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . 1 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . . . . . |
$$ | . . 3 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 4 . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
But, plausible as it looks, it is much better for White, IMHO, because Black's influence is being restrained, while White is getting the chance to enclose the corner.
However, there is another way to play (see
Get Strong at the Opening, No. 33).

Not the best possible example, but es klappt
- Click Here To Show Diagram Code
[go]$$c Not the best possible example, but es klappt
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . . X . . . |
$$ | . . O X . . . . . . . . . . . . . . . |
$$ | . . X 2 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 1 . . . . . . . . . . . . . . . |
$$ | . . . , . 3 . . . , . . . . . X . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
The point here is that Black is putting his side of the original exchange hard to work, and the overall effect is very efficient.
And this brings me to understand, just a little more deeply, that every exchange or skirmish has a meaning, and you need to play so that you do not lose your meaning or so that you cause the opponent to lose their meaning.
If you enclose a corner, it means you have spent two moves in one place, while the opponent has perhaps taken two moves across a larger area. Therefore, to make full value of your enclosure, you have to challenge your opponent's wider, but probably thin, position, using your enclosure as a base. If you do not exploit your side of the bargain, then you are living a life of dissipation; and if you cannot exploit it, then you've been had!
A better example is this one, No. 92 from
Get Strong at the Opening. If you are interested to see, there are other problems in the same part of the book with the same basic idea.

Putting thickness to work
- Click Here To Show Diagram Code
[go]$$c Putting thickness to work
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . a . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . O O X X X X . . , . . . . . O . . . |
$$ | . O . O O X . . . . . . . b . . . . . |
$$ | . O . O X . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Now, based on my misunderstanding of O Meien's "zone press park" thingie, which I have only been able to glean from the internet as I don't have a copy of the book, and misguided by the proverb about playing far from thickness, I have often played moves like a in the past. After all, b is all of six lines away from Black's thickness, while a is sensational nine lines distant from the star point in the upper right.
But, the best move is b. It makes the thickness work! Therefore it justifies the bargain black made in the lower left earlier.
It's hard to imagine it happening in a position like this, but I'm sure most of you have shared the painful experience of having had thickness, and then playing in the wrong direction. Eventually, the thickness turned to heaviness, and there was no choice but to make eyes, which is the ultimate humiliation for a once-thick and mighty group.
It could be that a is in fact bigger than b, at least territorially, but b is more urgent, because it prevents black's exchange in the lower left from becoming pointless. And, didn't Jim Kerwin 1p say something like an urgent move was one that prevented one of your earlier plays from becoming meaningless?
It is said that territory is like cash in hand, while thickness is like money in the bank. I think there's a lot of depth to that statement. If you have invested money, you have to wait for a long time before you get dividends for it; but the investment grows (hopefully!). If you don't invest, but let the thickness just sit there, then it will become less and less valuable, like money under the mattress. That's why my old notion of "Deadweight Value of Thickness" is probably invalid. (You can read my thoughts about that on Sensei's Library, should you be so inclined.) If you have cash, you have to keep getting some more once what you have is spent. The difference is that with money in the bank, you make the money do the work; with cash,
you have to do the work.
And isn't that so true of go? If you make a thick game, you can feel as though you are behind for a long time, but if you have put the thickness to work, little by little the returns start to come in. If you play territorially, you start off with easy money, but as the game wears on, you have to work harder and harder; after all, the two stones you spent on your enclosure (for instance) cover only a small area, while the opponent's stones on the side cover a greater area.
Small wonder, then, that Takemiya finds his style "natural", while people like Cho Chikun or O Rissei are noted for the skills at sabaki and shinogi.