In this answer, I'll first establish that this assumption about the operating principle of darshinan taama dekra doesn't fit with the sources, and then offer three possible resolutions to the difficulty.
There is a big Talmudic dispute whether we interpret the reasons behind commandments, with Rabbi Shimon famously endorsing the position. However, even those who say we don't so interpret often discuss reasons for commandments, and it is meritorious to do so. The core difference is whether the interpreted reason can be used to qualify and restrict the application of the law. For instance, if the purpose of prohibiting taking the garment of a widow as a pledge (because otherwise, you need to return it at night because she will have nothing in which to sleep, and we don't want this to occur for other reasons), this should not apply to a rich widow. See Sanhedrin 21a for this example.
דתניא אלמנה בין שהיא ענייה בין שהיא עשירה אין ממשכנין אותה שנאמר (דברים כד, יז) לא תחבול בגד אלמנה דברי רבי יהודה רבי שמעון אומר עשירה ממשכנין אותה ענייה אין ממשכנין אותה ואתה חייב להחזיר לה ואתה משיאה שם רע בשכנותיה
As it is taught in a baraita (Tosefta, Bava Metzia 10:3): In the case of a widow, whether she is poor or whether she is wealthy, one may not take collateral from her for a loan, as it is stated: “You may not take the garment of a widow for a pledge” (Deuteronomy 24:17); this is the statement of Rabbi Yehuda. Rabbi Shimon says: In the case of a wealthy widow, one may take collateral from her. But in the case of a poor widow, one may not take collateral from her, because you are obligated to return it to her, and you will give her a bad name among her neighbors.
To put your assumption to the test, according to Rabbi Shimon, how could he say that the ethical consideration of this poor widow be the concern? After all, this religious obligation does not apply to gentiles! If God wanted to protect widows, it would have applied to Jewish lenders and borrowers, and gentile lenders and borrowers alike! Yet, Rabbi Shimon still says what he says. This is, in my view, a proof by contradiction that the assumption underlying your question is somehow false. (Why it would be false is a separate question, but the proof by contradiction takes statements by Rabbi Shimon, the main proponent of darshinan taama dikra, as axiomatic, so any argument which then undermines these statements must be false. You can of course feel free to question Rabbi Shimon as well, and not take it as axiomatic. You could also argue that this reason regarding the poor widow is not ethically guided, but I don't see that as convincing.)
As to why ethically-guided commandments would only apply to Jews and not gentiles, I can offer a few suggestions.
a. It could be that while God desires the result, He is not imposing it as a requirement upon all people, only those who opt in to the more difficult level of obligations. There are different and good ways of living one's life, and righteous gentiles fulfill one level, and imposing all sorts of ritual obligations on gentiles is not what God intended, just that they broadly live ethical lives.
b. The point is process rather than result. If indeed the purpose of shechita is that it is less painful (though I don't necessarily endorse this as the reason), God wants the Jewish nation to develop their trait of compassion, and slaughtering animals in this more compassionate manner helps develop that trait.
c. There are several reasons for the commandment, and we might say that minimizing pain is one of the reasons. See Ein Ayah (to TB Shabbos 23b, §26) by Rav Kook, that there may be multiple reasons for the commandment. (In shiur, I heard this idea developed, that we may not know all the reasons for a commandment, which is why we don't rule like Rabbi Shimon to use this to limit the application of the law. After all, perhaps a different reason applies, and we don't even know all of the reasons.)
Taking this idea and running with it, it could be that the ethical component is the reason for the particulars of the mitzvah. In other words, requiring that Jews slaughter their animals in a prescribed manner has several effects, such as distinguishing their diets from the diets of the neighboring nations (so that they won't intermarry). Why did God choose this specific way of changing the diet? Because it is also more ethical, and reduces the pain of the animal. Or, for another reason, it enhances health - not that it will kill the stranger or foreigner, but it will reward those who follow His commandments and promote His ethics, by giving them fewer health problems. That does not mean that He will impose upon the gentiles that they may not eat this food because it is less healthy. And it is one of several reasons which sum up to a commandment imposed upon Jews.