Why was Noah told to load seven of clean livestock and only two of unclean wild animals (Gen 7:2)?

This seems to have a very straightforward practical answer: because of the importance of the former for food, and because he would have to sacrifice some of them. Wild animals only needed to be preserved, but large and healthy herds needed to be preserved, and it seems reasonable to suppose that Noah and his family ate of those herds for the year that they were on board the Ark (by the reckoning in the ESV Study bible, 370 days). That these “clean” animals—cleanliness being a notion known to God, but not yet introduced in the Bible record to Noah—would be needed for sacrificing can be found at Gen 8:20.