Is there any practical implication to the Avot's being priests?

Question

According to various sources, Malkitzedek was punished for blessing Avraham before blessing Hashem by having his "priesthood" status taken away and placed on Avraham. This status is then passed down until it is limited to Aharon's family.

In the interim, though, that status of Kehuna (in some form) resided with the avot, starting with Avraham. Was there any practical implication in how they lived their lives because of that status? Were they even aware of it?

Did that status limit their behaviors in ways that are connected to being "kohanim"? Some were clearly tamei met (including Levi) but I don't know if a Kohein can have multiple wives.

Is there any discussion of the status of "priest" after Avraham receives it and before it is discussed in terms of Moshe and Aharon?

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I see the priest status as different from something like kingship which would someday go to Judah's line. Before that, there wasn't a king. But Malkitzedek, and by that understanding, Avraham, already triggered the priest status.

I also understand that one could say that the laws of kehuna were not yet given so there would be no limitation on behavior before that took place, but if the avot kept the Torah in some sense, would any of the priestly laws be included?

Answer 1

Rabbi Philip Biberfeld in Universal Jewish History, vol 2, argues that there were at least some practical implications for priestly roles in how the Avot lived their lives:

"From Biblical records one can deduce that originally neither priests nor temples existed. Worship was conducted by the head of the family and entrusted to the firstborn son...In the house of Isaac, Esau was in charge of sacrifices. The neglect of those responsibilities induced Jacob to buy the birthright from him..."

It seems that according to this, at least one of the reasons Yaakov bought the birthright from his brother was because he thought someone had to assume responsibility for the priestly role in the family.

"Places of worship, consisting primarily of an altar, were erected on certain occasions...Abraham, as is repeatedly mentioned, built altars that were not intended for sacrifices but were places of prayer where he also propounded his teachings. These altars were close to his tents and were the places of his daily prayer. Pillars were erected by Jacob at sites of divine revelations to commemorate their occurrence. (pg. 49)

And according to this, the Avot erected altars and pillars out of their duty of creating places of worship. Interestingly, Yaakov only began erecting pillars and altars after receiving the birthright. Avraham didn't have to receive the high priesthood from Malki-tzedek to erect altars because, as head of his branch of the Bnei Terach clan, he was already in the role of a high-ranking priest.