Dear Sholem,

Great to hear from you. Excellent question.

Tosfos in Bava Kama [1] explains that it would be shameful to the deceased person that his burial involved a violation of Shabbos even when the work was done by a goy. The Magen Avraham [2] cites Ramban in Toras ha'Adam as saying a similar idea, even adding a couple of points:

a) It is forbidden to ask a gentile to perform even a rabbinic prohibition for the sake of the deceased. For example, carrying the departed to be placed in a grave that was already dug before Shabbos.

b) There is less room to relax prohibitions that are well known as violations of Shabbos (unlike carrying into a Karmelis which people understand is not really a Shabbos desecration).

I hope this helps. May you continue to attain greatness in Torah learning and Yiras Shamayim!

Gmar Chasimah Tovah,

Yishai Rasowsky

Sources:

1. https://dafyomi.co.il/bkama/tosfos/bk-ts-081.htm#:~:text=%D7%90%D7%9C%D7%90%20%D7%9C%D7%A4%D7%99%20%D7%A9%D7%94%D7%95%D7%90,via%20a%20Nochri%20...

2. https://www.sefaria.org.il/Magen_Avraham.311.13?lang=he&with=all&lang2=he#:~:text=%D7%9B%D7%91%D7%A8%20%D7%94%D7%90%D7%A8%D7%99%D7%9A%20%D7%91%D7%96%D7%94,%D7%A9%D7%9C%20%D7%93%D7%91%D7%A8%D7%99%D7%94%27%20%D7%A2%D7%9B%22%D7%9C

Dear Sholem,

You may have seen the Mishnah Berurah's way of expressing this issue regarding your question. I understand him [1] to mean that since the greatest issue at stake is showing honor for the dead (which is why we try to get the Meis buried as soon as possible even if that means asking gentiles on Yom Tov), then since Shabbos and Yom Kippur are viewed by people as stricter days, and thus when Melachah done on Shabbos or Yom Kippur for Meis, even by gentiles, it actually detracts from Kavod ha'Meis rather than adding to it, therefore it is better not to ask gentiles to bury the body, unlike Yom Tov.

It reminds me of the regular law of hastening a burial, even on a regular weekday. This is done to impart honor to the departed. Since that is the reason, it therefore follows that delaying is actually permitted when it will translate into a greater Kavod for the Meis [2].

I see now that the Ramban deals more expansively with your question [3], and offers several reasons to distinguish between Shabbos and Yom Tov, as follows:

A. Many types of Melachah are already permitted on Yom Tov (e.g. cooking and carrying). Therefore, the prohibition to perform Melachah on Yom Tov is less well known to people, unlike Shabbos on which people know that all Melachah is strictly forbidden. The implication being, that when a gentile does Melachah for us on Yom Tov by burying the dead, Chazal felt there was less of a concern that it would lead to a Zilzul of the day, unlike on Shabbos which would be more sensitive to Zilzul. [This is how the Oz v'Hadar Mishnah Berurah (Siman 526, Seif 3) explains this part of the Ramban.]

B. Just like Machshirin are permitted for Simchas Yom Tov (e.g. extiguishing a burning log that is making your house uncomfortably smokey -- see Beitzah 22), so too burying the Meis makes your house more comfortable to live in. So Chazal did not forbid asking a gentile in this case.

C. Since burial will provide more respect for the dead, therefore Chazal chose not to forbid Amirah l'Nochri on Yom Tov, since Melachah on Yom Tov in the first place is only an Isur Lav, unlike on Shabbos which is an Isur Sekilah (see Beitzah 21 and Yevamos 114 for a precedent for this Chiluk), even though normally Chazal did not distinguish between these two levels, since they are both Torah prohibitions (as the Ramban himself cites from Yevamos 94).

D. It would be too shameful for the Meis himself if Melachah was done for him on the holy day of Shabbos (even by gentiles).

As we discussed, it the last answer that was apparently accepted by Tosfos, as well as Magen Avraham and Mishnah Berurah.

Best wishes,

Yishai Rasowsky

Sources:

1. https://www.sefaria.org.il/Mishnah_Berurah.526.17?lang=bi&with=Shulchan%20Arukh,%20Orach%20Chayim&lang2=en

2. https://www.sefaria.org.il/Shulchan_Arukh%2C_Yoreh_De'ah.357.1?lang=bi&with=Commentary&lang2=en

3. https://hebrewbooks.org/pdfpager.aspx?req=41324&st=&pgnum=41&hilite=