See Chatam Sofer on Sabbath (74a in the standard pagination), in the name of his grandfather — based on the Talmud there, it seems the reason is that something that has already been used for a commandment already has an importance of its own, and is preferable to something new.
And in Ein Ayah on tractate Berakhot 39, he explains that the Talmud is coming to teach us that wholeness in quality is preferable to wholeness in quantity; see there.

I didn’t find anything at all in Chatam Sofer on Sabbath 74.
https://hebrewbooks.org/pdfpager.aspx?req=19920&st=&pgnum=43

Ein Ayah is on Berakhot 39.
https://he.wikisource.org/wiki/%D7%A2%D7%99%D7%9F_%D7%90%D7%99%D7%94_%D7%A2%D7%9C_%D7%91%D7%A8%D7%9B%D7%95%D7%AA_%D7%95_%D7%9B%D7%94

A nice idea, but it doesn’t explain the Talmud. It makes sense that it is better to raise one great Torah scholar than two mediocre ones. But for example with charity, there is clearly no reason to give 200 shekels to one poor person instead of 100 shekels to each of two poor people. So why are objects different from poor people? And besides, do objects feel anything when a commandment is performed with them? It is nothing but puzzling. And kabbalistic matters are not, to me, a satisfactory way to explain the Talmud.
In the Talmud, we are speaking either about a benefit to the object, or a benefit to the second commandment, or a benefit to the person. A benefit to the object is puzzling, and also similar to the poor people I mentioned — on the contrary, since a commandment has already been done with it, let us now take a different object. A benefit to the commandment is also an incomprehensible idea, though perhaps the kabbalists would be happy to hang all sorts of heroic banners on that. So a benefit to the person — what Rabbi Michi above called a psychological matter — is what remains, and that seems likely.

My apologies. It’s not in Chatam Sofer. Rather, it’s in the responsa Chatan Sofer, siman 68 (in the name of his grandfather the Chatam Sofer on the passage in Sabbath 74).

https://hebrewbooks.org/1533

Thanks. But the truth is that I don’t really understand what is written there. I read it quickly, and I’m writing without sufficient analysis.
https://hebrewbooks.org/pdfpager.aspx?req=1533&st=&pgnum=212

A. He asks why with a Hanukkah lamp one may light with a used wick but not with a used lamp. That seems easy enough to explain, since a used wick is better than an old wick. That is why people singe the wick for Sabbath candles. But a used lamp is perhaps stained and looks degrading. And it is not similar to the bread of the eruv, where no use was made of the bread itself.
B. He asks why, if a curtain-sheet got a hole, they sew up that same sheet, whereas if two threads happen to be tied in the same place, one does not untie one and leave it, because one does not do that for an earthly king. What kind of question is that? In the case of the sheets, this is a repair, and one would do that even for an earthly king. In the case of the threads, the issue is leaving things in a defective condition, and that too one would not do for an earthly king. Also, a thread and its work are a minor matter and not at all comparable to replacing an entire sheet.
C. The continuation there also requires further examination, and I’m too weary to elaborate.
D. His interpretation in Tractate Soferim is unfortunately also strained in itself, as anyone can see with his own eyes, and it too proceeds by way of pilpul that seems quite far from the plain meaning. If only I knew what pleasure you found in it.

In any case, there is no explanation there of the reasoning itself, only an export of this principle of “since” as it stands into other contexts.

First of all, be well — I didn’t mean for you to read the entire responsum, only the section with the novel point in the name of the Chatam Sofer.

As for the point itself, this is how I understood it: the Talmud asked regarding “untying” in the case of two threads, that this is not something one does for an earthly king. Later it asked from “tearing” — if a sheet got eaten by a worm, one tears it and sews it. Tearing is not just minor unravelling. Tearing is done in order to repair, by enlarging the hole, and perhaps there is some kind of repair here that is not elegant craftsmanship, and even that one does not do before an earthly king. Rather, if a worm ate it, one throws it out and replaces it. And so he innovated that from here we learn the importance of the advantage of something already used, in the vein of “since,” etc. (That’s what I enjoyed!)
Remember that the Chatam Sofer lived in days when there were kings, and he knew their ways and customs. (And I think even nowadays it is like that.)

First, on its own terms, as I wrote, it does not seem like a real question. There is no comparison whatsoever between a standard repair (in a sheet) and leaving a defect in place (in a thread; see Rashi there). With threads too, even for an earthly king, the weaver would invest another two minutes so it would look nice. And with a sheet, even for an earthly king, one repairs it.
Second, just think about it: such a simple question in the Talmud itself, within just a few adjacent lines, and all the medieval authorities ignored it until along came the Chatam Sofer? So clearly, in the plain sense, there is no difficulty at all, and perhaps he said it merely to broaden the discussion, by way of pilpul. And apparently not for nothing did the Chatam Sofer not write this in his novellae. (And the entire responsum there in Chatan Sofer really is of one piece. It is not that he relied on this for a halakhic ruling; perhaps the whole thing there is just for dialectical discussion.) Besides, explanations that arise from the context itself are more satisfying than ones based on some principle drawn from somewhere else, not mentioned here at all, as though the Talmud simply assumed it to be obvious. Especially since that principle itself is not understood either, so what is the use of building structures with it? On the contrary, all we have in it is the novelty itself.