If Aphrodite is the daughter of Ouranos and Gaia, why is she not a Titaness, Giantess, Erinye, or Melia? Is there a specific reason for her to be a goddess if all other gods are descendants of Cronus and Rheia?
She isn't the child of Ouranos and Gaia. There are two chief myths to her birth. The first and oldest is found in Homer, where she is the daughter of Zeus and Dione. As the daughter of Zeus and another god, she is fully divine.
Hesiod in his Theogony instead makes her the daughter of Ouranos, but not of Gaia. Instead she was born when his castrated testicles fell into the sea. This is an etymological aetion connecting her name to sea-foam (ἀφρός, aphros). Hesiod's Theogony likely comes after Homer's Iliad, though that is a much debated topic. (In particular, West and Janko place Hesiod first.)
However, your assumption isn't true. Athena, Apollo, Artemis, and Dionysus weren't the children of Cronus and Rhea, yet all are considered gods. In fact, all of the above would be "gods." Titans, too. What makes the Dodecatheon, the pantheon of twelve gods, Olympians is that they lived on Olympus. Hades, the brother of Zeus (and Poseidon, Hera, Hestia, and Demeter) did not live on Olympus, so he does not have that designation. Aphrodite does, so she's Olympian.
The Greeks also weren't too big of sticklers on this point. Greek mythology is not a cohesive whole, but in constant flux. With each new poet, various traditions became codified, but they often conflicted. This is just one of those times.