In my opinion one huge advantage is the data size reduction needed for few-shot learning.
Collecting and cleaning a dataset is extremely costly and often users underestimate the necessary work load to create a dataset such as ImageNet.
Another argument for few-shot learning might be that “a baby doesn’t need to see 100k images of a giraffe to recognize one”. So the argument is that the sample efficiency of a lot of DL models is bad and has to be improved.