ASTM D882 is for plastic films. For thins films of many other materials, dog-bone specimens are more commonly used.
The deformation of dog-bone specimens is not homogeneous through the length of the full specimen. That means that the cross-head displacement of the testing machine is not necessarily equal to the displacement of the gage region. As a result, you will need some sort of extensometer to measure the change in length of the specimen which makes the test a bit more complicated.
Of course, it can be argued that the deformation is not homogeneous in a rectangular specimen either - which is why you run into breaks at the grips.