Why Were The Levi’im Working?

The Torah explains that Hashem was justified in taking the Levi’im, because they were instead of the bechorim, who were consecrated when Hashem killed the Egyptian firstborn. Why does the Torah seek to justify Hashem choosing the Levi’im; had they not stood by Him when the rest of the Jews worshiped the Egel? Why did they need to be in place of the Bechorim?

One thought we had that gaining privileges was what the Levi’iim deserved, but they received obligations too; they were obligated to work for Hashem, whether they wanted to or not. This is no bonus, nor loyalty prize. So the Torah explains the element of obligation; they were supplanting the Bechorim, who were obligated to Hashem, and that obligates the Levi’im.