There are all sorts of reasons one can offer for this, such as the focus here being that it not be consumed, even though it is not going on the mizbeach. But why not cover the blood with dirt?
Rav Yonasan Eibeshitz offers a creative answer: that this was to counter an foreign and incorrect theological belief, that of the nations in the country of Andian, that the beheimah has an elevated soul, and they buried the blood when the animal died. You might want to do like them, and so the pasuk warns against it.
While creative, it seems rather farfetched. I might suggest that on a peshat level (but against the established halacha) that the point is the spilling of the blood rather than sprinkling or eating, and the pasuk in Vayikra 17:13:
|יג וְאִישׁ אִישׁ מִבְּנֵי יִשְׂרָאֵל, וּמִן-הַגֵּר הַגָּר בְּתוֹכָם, אֲשֶׁר יָצוּד צֵיד חַיָּה אוֹ-עוֹף, אֲשֶׁר יֵאָכֵל--וְשָׁפַךְ, אֶת-דָּמוֹ, וְכִסָּהוּ, בֶּעָפָר.||13 And whatsoever man there be of the children of Israel, or of the strangers that sojourn among them, that taketh in hunting any beast or fowl that may be eaten, he shall pour out the blood thereof, and cover it with dust.|
which was about wild animals and fowl was only so because of an assumption that any beheimah would be brought to the Temple. But once we equate these particular beheimot to be as the gazelle and the hart, all their laws are equated.
Working on the level of halacha, we might say that since in other contexts the blood is sprinkled on the mizbeach, if we accord any level of respect to this blood by ritually covering it, it might develop into a cult practice on personal altars.