The Torah is explicit about a rationale for [at least some part of] this command:
וְיִֽהְי֥וּ לְא֖וֹת לִבְנֵ֥י יִשְׂרָאֵֽל
let them serve as a symbol to the people of Israel
זִכָּר֞וֹן לִבְנֵ֣י יִשְׂרָאֵ֗ל לְ֠מַעַן אֲשֶׁ֨ר לֹֽא יִקְרַ֜ב אִ֣ישׁ זָ֗ר אֲ֠שֶׁר לֹ֣א מִזֶּ֤רַע אַהֲרֹן֙ ה֔וּא לְהַקְטִ֥יר קְטֹ֖רֶת לִפְנֵ֣י ה' וְלֹֽא יִהְיֶ֤ה כְקֹ֙רַח֙ וְכַ֣עֲדָת֔וֹ
It was to be a reminder to the Israelites, so that no outsider—one not of Aaron’s offspring—should presume to offer incense before the LORD and be like Korah and his band.
Regarding the first one Rashi comments
ויהיו לאות. לזכרון שיאמרו אלו היו מאותן שנחלקו על הכהונה ונשרפו
ויהיו לאות THEY SHALL BE AS AN אות — The word לאות is the same as לזכרון, something to be mentioned (cf. Exodus 13:9) — that people will always say: These plates were from (once belonged to) those who raised dissension about the priesthood and were burnt.
He understands the signal to be a reminder not to disagree [contentiously] with the [institution, responsibilities and privileges of] the priesthood, which is presumably a fight anybody can pick, not just other kohanim. This is in keeping with his explanation of the second one, namely,
ולא יהיה כקרח. כדי שלא יהיה כקרח
ולא יהיה כקרח means in order that he be not as Korah.
Here too, publicly protesting authority and societal order, or general rabblerousing - i.e. being like Korach - are activities anybody can engage in, so Rashi consistently explains this as the point the copper plating would make. It is reasonable to assume, seeing these comments of his, that Rashi concluded when Hashem commanded the plating to be made for "the mizbe'ach" that it was the outer, more visible one.1
According to Rashi, the command was to turn them into coverings for the copper altar in order to remind Israel not to attempt a repeat performance of bringing the incense inappropriately.
Your point that as much as B'nei Yisra'el are mentioned as a broader collective twice in this command, the reminder about burning incense properly doesn't relate directly to them is well-taken. But it comes from the Torah itself in the second pasuk quoted above, not from Rashi. Once we have established that the discouraged behavior is emulating Korach with respect to his [ilk's] confrontation with the priesthood, it stands to perfectly good reason that those closest to the action in question, would also be reminded not to fall victim to the exact same temptation that caused his downfall.
I don't think we should understand the os and zikaron here to be practical impediments to a person who is literally on their way to transgress the proper burning of incense. After all, that is not how the pans were being used by Korach and friends to begin with2. Rather, Rashi and a theme of midrashim on this topic understand the "sign" to be an educational one, which is valuable to all sectors of the nation though perhaps in different ways, as seen from the p'sukim above.
The Chizkuni goes as far as to say
הא למדנו שהדבור למשה שיאמר לאהרן שיהא הרואה שואל הרי כתיב מזבח אדמה תעשה לי שהיו ממלאים את חללו עפר אם כן מה טיבו להיות לו גג מנחושת והנשאל משיב גג זה נעשה ממחתות קרח ועדתו שהיו מערערין על הכהונה וכל העם ישמעו וייראו לערער עוד
This teaches us that the statement to Moshe that he'd tell Aharon was so that the observer would ask "But it's written, 'An altar of earth you should make for Me' - that we'd fill its cavity with dirt! If so, what's the point of its having a copper covering?" And the one who's asked can respond that this covering was made from the firepans of Korach and his gang, who contested the priesthood. And [thus] all the nation will hear and fear contesting again.3
as if the lesson was meant to be taught before the plating was even made or installed, when Moshe was teaching about how it would be done and why.
1 According to the N'tziv in Ha'mek Davar (on the spot), it was El'azar who came to this conclusion, but on the basis of a slightly more obvious fact that the pans were copper and so was the outer mizbe'ach so it would be a good fit.
2 Not exclusively, although it should get the literal message across too, for people like Uziyahu, who tried and suffered the consequences.
3 Mi Yodeya community translation