What strikes us today as bizarre might not have done in the 18th century and earlier. After all in poetry, and this is a type of poetry, anything can happen. Talking animals are fairly common. Some of the ballad makers were quite simple people who didn't necessarily put in a great deal of thought or sense, and often were just imitating a simple idea from elsewhere, classical mythology, folk-tale etc.

At the same time as giving animals speech and intelligence of a human sort, they also gave them human desires, such as a golden cage, golden wings, silver combs etc. Our ballads are not that far removed in content and ideas from the folk tales which abound in such things.

The parrot in Lady Isabel and the Elf-Knight could well be an echo/corruption of the dove that warns sometimes the knight, sometimes the maid, as they ride off together from her father's hall, in early German versions. Such a ballad that is known all over Europe has been in and out of oral tradition and print and through the hands of antiquarians and poets for centuries. Then you have to factor in the borrowings from one ballad to another. Talking creatures and incongruities shouldn't surprise us.