A half adder has less components, and may therefore be cheaper.
So, in cases where all you need is a half adder, it may be more
convenient to use a half adder. Or it may be more convenient to
mass-produce only the full adders, since a full adder can work as a
half-adder as well.Also, in introductory electronics textbooks, the
half-adder would be introduced first, just because it is
simpler.