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One could answer that the kohanim might not encourage people to bring a korban olah for which they did the work but did not receive any meat to eat in return. However, generally we say that failure to receive something is not equivalent to losing money.
Rav Yaakov Kaminetsky (in Emet L’Yaakov) allows one point to answer the other. The mizbeach had to always have a korban on its ever-lit fire. When one was running out, the kohanim would bring a korban olah to continue. Aharon, being a great lover of Jews, not only from a spiritual perspective but also in regard to their physical needs, was concerned with the expense to the Jewish people of continuously providing korbanot olah. Since their loss was like his loss, the Torah encouraged the kohanim not allow this concern to hinder their work. It also stressed in this context that a single korban olah would last on the mizbeach all night and into the morning, and thus the expenses would not be prohibitive.
The kohanim’s concern about the korbanot’s expense to K’lal Yisrael also found expression in a negative light. The gemara (Sukka 56b) tells of sanctions to the Bilga group of kohanim because words of an apostate from their midst made it evident that some of them complained that the mizbeach was using up Jews’ funds. Although this concern could be abused, the choice of Aharon’s family for service in the Beit Hamikdash was apparently not despite the fact they were concerned for their fellow Jew’s physical, in addition to spiritual, well-being, but at least partially because of it. Even within the realm of worship of Hashem, "spiritual needs" are to be balanced with physical ones. That balance is not to be achieved because of lack of passion about either state but because one is passionately concerned about both. As Rav Kaminetsky posits, Hashem Himself was concerned with Bnei Yisrael’s finances and took steps to limit the number of olot needed.
Also within the realm of halacha, Hashem’s main concern in the absence of the Beit Hamikdash, we are told that Hashem wants to spare Israel’s money (Chulin 49b). This is the rationale for many leniencies when monetary loss is involved. In that context as well, it is not out of a lax approach to halacha that a rabbi could and should be appropriately lenient but out of a justified concern for his fellow Jew’s physical well-being.

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